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Invariant measures via inverse limits of finite structures

Nathanael Ackerman, Cameron Freer, Jaroslav Nešetřil, Rehana Patel
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
These measures are constructed from inverse limits of measures on certain finite structures.  ...  infinite structures, that are invariant under all permutations of the underlying set that fix all constants.  ...  Work by JN has been partially supported by the Project LL-1201 ERCCZ CORES and by CE-ITI P202/12/G061 of the GAČR.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2015.07.006">doi:10.1016/j.ejc.2015.07.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6rjqirirtrdkbnem2g646iul7q">fatcat:6rjqirirtrdkbnem2g646iul7q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180723023958/https://manuscript.elsevier.com/S0195669815001729/pdf/S0195669815001729.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fe/60/fe60616e01792e21f3239501d9a5b3d09f9dbcf2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2015.07.006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Thurston boundary of Teichmüller spaces and the commensurability modular group

Indranil Biswas, Mahan Mitra, Subhashis Nag
<span title="1999-04-12">1999</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k76rcy45xne6jlpmdtcz26fvze" style="color: black;">Conformal Geometry and Dynamics</a> </i> &nbsp;
Using this result, an inductive limit of Thurston compactified Teichmüller spaces has been constructed, where the index for the inductive limit runs over all possible finite unramified coverings of a fixed  ...  This inductive limit contains the inductive limit of Teichmüller spaces, constructed by I. Biswas, S. Nag and D.  ...  Indeed we can now show the existence of an inverse limit measure on the limit object, (a measure whose conditional expectations fit coherently).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s1088-4173-99-00036-3">doi:10.1090/s1088-4173-99-00036-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pisau4zu4bhxjgux6l6ui7mre4">fatcat:pisau4zu4bhxjgux6l6ui7mre4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200812202226/https://www.ams.org/journals/ecgd/1999-03-04/S1088-4173-99-00036-3/S1088-4173-99-00036-3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/70/ca704db7e4995c64a61ceb9f5ad8f566d8acfe00.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s1088-4173-99-00036-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Thurston boundary of Teichmüller spaces and the commensurability modular group [article]

Indranil Biswas, Mahan Mitra, Subhashis Nag
<span title="1999-02-26">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Using this result, an inductive limit of Thurston compactified Teichmüller spaces has been constructed, where the index for the inductive limit runs over all possible finite unramified coverings of a fixed  ...  This inductive limit contains the inductive limit of Teichmüller spaces, constructed in BNS, as a subset.  ...  Indeed we can now show the existence of an inverse limit measure on the limit object, (a measure whose conditional expectations fit coherently).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9902153v1">arXiv:math/9902153v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c2wvoduznveonksyz7dbathriu">fatcat:c2wvoduznveonksyz7dbathriu</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9902153/math9902153.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9902153v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 29 of Mathematical Reviews Vol. , Issue 2002B [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Let vy be a left-invariant measure on G. From a study of v x y the right-invariance and inversion- invariance of v-null sets is established.  ...  Measurability is via Carathéodory’s splitting criterion. The measurable sets are shown to constitute a a-algebra which includes all Borel sets.  ... 
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Contents [chapter]

<span title="2021-11-22">2021</span> <i title="De Gruyter"> Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps </i> &nbsp;
15.3 20.5 27.9 Topological exactness | 80 7.2.3 Third and final stage: entropy of a system | 186 Definition of topological pressure via open covers | 350 13.4 Construction of invariant measures from quasi-invariant  ...  invariant measures | 212 Inverse branches | 108 The variational principle | 371 Almost periodicity of normalized transfer operators 15.4 A digression into geometric measure theory 21.4 Multifractal analysis  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110702682-toc">doi:10.1515/9783110702682-toc</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6bgmt6gqbzdxpgmmdwnghdebaq">fatcat:6bgmt6gqbzdxpgmmdwnghdebaq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220428141216/https://www.degruyter.com/document/doi/10.1515/9783110702682-toc/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/45/c1/45c1c1edc9c6f27043dbb747524a3d67ce929fc7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110702682-toc"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> degruyter.com </button> </a>

Spectral Structures and Topological Methods in Mathematical Quasicrystals

Michael Baake, David Damanik, Johannes Kellendonk, Daniel Lenz
<span title="2018-12-18">2018</span> <i title="European Mathematical Publishing House"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mnv35em3uvgxdkcbx2cvykhugu" style="color: black;">Oberwolfach Reports</a> </i> &nbsp;
made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of  ...  For general tilings, inverse limit descriptions exist via various models [1, 3, 7] , but without specific structure these are principally of theoretical use.  ...  Most lines of approach start from one or other of the observations that Ω can be (a) described (up to shape equivalence -see later) as an inverse limit of convenient finite CW complexes (approximants),  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4171/owr/2017/46">doi:10.4171/owr/2017/46</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/les27wbaurbpdazguku2nabbay">fatcat:les27wbaurbpdazguku2nabbay</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200309071618/http://dro.dur.ac.uk/23292/1/23292.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d7/af/d7af56830d0a84fca430f6be98514bb8d1b8c1e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4171/owr/2017/46"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Inverse identification of the material parameters of a nonlinear concrete constitutive model based on the triaxial compression strength testing

Petr Král, Petr Hradil, Jií Kala
<span title="2016-12-15">2016</span> <i title="Gruppo Italiano Frattura"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kaq2rz4xxvfszkkjuugxyp64iy" style="color: black;">Frattura ed Integrità Strutturale</a> </i> &nbsp;
When applying such parameters, the resulting response of the structure obtained from a computer simulation is very similar to the real response of the structure based on the related experimental measurement  ...  The aim of this paper is to perform the inverse identification of the material parameters of a nonlinear constitutive model intended for the modeling of concrete which is known as the Karagozian & Case  ...  Financial assistance was also received via project FAST-J-16-3744 "Optimization of the parameters of nonlinear concrete material models for explicit dynamics"; this instrument was structured and guaranteed  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3221/igf-esis.39.05">doi:10.3221/igf-esis.39.05</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f4nmvwbenre3jjj4yzkc4gyoam">fatcat:f4nmvwbenre3jjj4yzkc4gyoam</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20181109031623/https://www.fracturae.com/index.php/fis/article/download/IGF-ESIS.39.05/1843" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/ce/aace4b87553f19d21721bcecb6878cf92c3af953.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3221/igf-esis.39.05"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

On invariant measure structure of ergodic discrete dynamical systems [article]

Anatoliy K. Prykarpatsky
<span title="1999-06-22">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method  ...  of invariant measure 3.1.  ...  The inverse is also true: due to the Birkhoff theorem [1] , if the mapping ϕ : M → M conserves a finite measure µ ϕ : A(M) → R + , mean valueas (1.1) are convergent µ ϕ − a.e. on M, and the set of convergency  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9906146v1">arXiv:math/9906146v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ri3yodkj3zcwdcydjnl64ml2ey">fatcat:ri3yodkj3zcwdcydjnl64ml2ey</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9906146/math9906146.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/54/52/545246fef57543d6b93fdba14d5d87336adccd5e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9906146v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Intrinsic metric on graded graphs,standardness,and invariant measures [article]

Anatoly Vershik
<span title="2013-12-27">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We define a general notion of a smooth invariant (central) ergodic measure on the space of paths of an N-graded graph (Bratteli diagram).  ...  In future, we will apply this new approach to the theory of invariant measures in combinatorics, ergodic theory, and the theory of C^*-algebras.  ...  There is a natural structure of inverse limit, or topological Cantor space, on the space T (Γ), defined via clopen, or cylinder, sets; we denote by A n the σ-field of cylinder sets of level n.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1312.7239v1">arXiv:1312.7239v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mz6zydgg5vheplvko62h64zcgy">fatcat:mz6zydgg5vheplvko62h64zcgy</a> </span>
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Contents [chapter]

<span title="2022-05-23">2022</span> <i title="De Gruyter"> Finer Thermodynamic Formalism – Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry </i> &nbsp;
of invariant measures from quasi-invariant ones | 449 13.5 Transfer operators | 452 13.6 Nonnecessarily-invariant Gibbs states | 455 13.6.1 Existence of eigenmeasures for the dual of the transfer operator  ...  states | 488 13.7.5 Invariant Gibbs states have positive entropy; pressure gap | 489 13.7.6 Absolutely continuous invariant measures for Shub expanding maps | 491 13.8 Finer properties of transfer operators  ...  continuous σ-finite invariant measures Definition of topological entropy via open covers Hausdorff dimension | 576 Ionescu-Tulcea and Marinescu inequality | 707 Real analyticity of Hausdorff dimension  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110702699-toc">doi:10.1515/9783110702699-toc</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ey2l7d5nijhtxp7uauo2sa33hq">fatcat:ey2l7d5nijhtxp7uauo2sa33hq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220608231051/https://www.degruyter.com/document/doi/10.1515/9783110702699-toc/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c6/95/c6957a239c3ea683c3e3faf814fe11d74477fcce.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/9783110702699-toc"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> degruyter.com </button> </a>

Page 4324 of Mathematical Reviews Vol. , Issue 84j [page]

<span title="">1984</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We show that this process is the ‘thermodynamic’ limit of mean field processes with finite volume. Finally, we show that invariant measures for finite volume converge, and we characterize the limit.”  ...  [Mean field process: existence, uniqueness, invariant measures and thermodynamic limits] Stochastics § (1981), no. 1-2, 93-106.  ... 
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Nonlinear Scale invariant Formalism and its Application to Some Differential Equations

Anuja Ray Chaudhuri
<span title="">2014</span> <i title="IOSR Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b4jiukqriresrjpdbs7dqmv5qi" style="color: black;">IOSR Journal of Mathematics</a> </i> &nbsp;
We report in particular some simple but nontrivial applications of this nonlinear formalism leading to emergence of complex nonlinear structures even from a linear differential system.  ...  This analysis is applied on a class of ordinary differential equations.  ...  We introduce scale invariant infinitesimals via a more refined evaluation of the limit   0 x in R .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9790/5728-10442737">doi:10.9790/5728-10442737</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3nkr3ng2vbaclilr3h2e6ddqyq">fatcat:3nkr3ng2vbaclilr3h2e6ddqyq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180601231916/http://www.iosrjournals.org/iosr-jm/papers/Vol10-issue4/Version-4/D010442737.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/86/0f/860f2822b5f5a31d0c9f4e8dd823c58e57eeb5e8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9790/5728-10442737"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On a new proof of the Prime Number Theorem [article]

Dhurjati Prasad Datta
<span title="2011-03-30">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Basic properties of some key concepts such as infinitesimals, the associated nonarchimedean absolute values, invariance of measure and cardinality of a compact subset of the real line under an IFS are  ...  A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further.  ...  We introduce scale invariant infinitesimals via a more refined evaluation of the limit x → 0 + in R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1103.6176v1">arXiv:1103.6176v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kk2q3b7nibe3tk3qdlywvz3f64">fatcat:kk2q3b7nibe3tk3qdlywvz3f64</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1103.6176/1103.6176.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/b1/f6b130ce734bff5228e27e647217a41253be5c90.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1103.6176v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 5256 of Mathematical Reviews Vol. , Issue 91J [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
of E such that there is no o-finite G-invariant measure on S.  ...  In the first we introduce finite models of the real line and seek to recover the analogues of the most classical definitions and properties of continuity, limits and differentiabil- ity of numerical functions  ... 
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Page 378 of Mathematical Reviews Vol. , Issue 85a [page]

<span title="">1985</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
“The paper only deals with linear, finite-dimensional, single- input/single-output, time-invariant systems that possess a stable inverse.  ...  For finite time, it is based on the use of pseudo-inverse, and, for asymptotic estimators, various approaches derived from Luenberger-type ob- servers are given.  ... 
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