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Page 2576 of Mathematical Reviews Vol. , Issue 2002D [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;
state of a system is from its equilibrium state [see J.  ...  to that of Axiom A attractors, with stationary states being invariant measures of Sinai-Ruelle-Bowen type (SRB measures).  ... 
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Page 198 of Mathematical Reviews Vol. 56, Issue 1 [page]

<span title="">1978</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 last chapter, “Ergodic theory of Axiom A diffeo- morphisms’’, contains the main results of the book. Let f: M—> M be a C? Axiom A diffeomorphism and let 2, be a basic set for f.  ...  The definition of the more general class of Axiom A diffeomorphisms is due to S. Smale. A point x ¢ M is nonwandering if UA U,5.f"U# @ for every neighborhood U of x.  ... 
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Page 1194 of Mathematical Reviews Vol. 52, Issue 4 [page]

<span title="">1976</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;
From this the author deduces conditions for an Axiom A diffeomorphism to be Bernoulli with respect to equilibrium states, when restricted to basic sets.  ...  A-B 276 (1973), A33-A35; MR 47 #6990]. ' S. J. Taylor (Liverpool) Bowen, Rufus Bernoulli equilibrium states for Axiom A diffeomorphisms. Math. Systems Theory 8 (1974/75), no. 4, 289-294.  ... 
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Equilibrium states for a class of skew products

MARIA CARVALHO, SEBASTIÁN A. PÉREZ
<span title="2019-05-14">2019</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t7qnh4dicrhptozut7w2ifbxua" style="color: black;">Ergodic Theory and Dynamical Systems</a> </i> &nbsp;
We present sufficient conditions, both on the skew products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability.  ...  We consider skew products on $M\times \mathbb{T}^{2}$ , where $M$ is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism.  ...  Besides, as σ × L is a C 1 Axiom A diffeomorphism and ϕ is Hölder, there is a unique equilibrium state of ϕ with respect to σ × L, which is a Bernoulli probability measure [7] since σ is topologically  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/etds.2019.32">doi:10.1017/etds.2019.32</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fz6dil7mlbbd7frx3mq5cao37e">fatcat:fz6dil7mlbbd7frx3mq5cao37e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200323091159/https://repositorio-aberto.up.pt/bitstream/10216/119630/2/331125.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/56/66/5666a46d439d211cb81ebe99a483c5080fa3355e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/etds.2019.32"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> cambridge.org </button> </a>

Equilibrium states for a class of skew-products [article]

Maria Carvalho, Sebastián A. Pérez
<span title="2018-08-06">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider skew-products on M×T^2, where M is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism.  ...  We present sufficient conditions, both on the skew-products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability.  ...  Besides, as σ × L is a C 1 Axiom A diffeomorphism and ϕ is Hölder, there is a unique equilibrium state of ϕ with respect to σ × L, which is a Bernoulli probability measure [8] since σ is topologically  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.01970v1">arXiv:1808.01970v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2boh4athdzac7mcrpoiv5zvdai">fatcat:2boh4athdzac7mcrpoiv5zvdai</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200911104255/https://arxiv.org/pdf/1808.01970v1.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/d3/7f/d37f9ae7d1a54b746fcc087e5dd8271c2fcb003d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.01970v1" 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 4167 of Mathematical Reviews Vol. , Issue 86i [page]

<span title="">1986</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 M be a closed orientable two-dimensional manifold of genus p> 1and let f: M — M bea diffeomorphism satisfying Axiom A* of Smale.  ...  Conditions are given for different center manifolds at an equilibrium point to have a nonempty intersection.  ... 
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Bernoulli equilibrium states for surface diffeomorphisms

Omri M. Sarig
<span title="">2011</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ebeyl2om5vbsrbiuzncpyjustm" style="color: black;">Journal of Modern Dynamics</a> </i> &nbsp;
Suppose f : M → M is a C 1+α (α > 0) diffeomorphism on a compact smooth orientable manifold M of dimension two, and let µ Ψ be an equilibrium measure for a Hölder continuous potential Ψ : M → R.  ...  We show that if µ Ψ has positive metric entropy, then f is measure theoretically isomorphic mod µ Ψ to the product of a Bernoulli scheme and a finite rotation.  ...  This was extended by Bowen [B2] to all Axiom A diffeomorphisms, using Parry's characterization of the measure of maximal entropy for a subshift of finite type [Pa] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/jmd.2011.5.593">doi:10.3934/jmd.2011.5.593</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p27uk7jkdvfqdbzkaeefs7epxm">fatcat:p27uk7jkdvfqdbzkaeefs7epxm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120123143736/http://www.wisdom.weizmann.ac.il/~sarigo/bernoulli.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/26/cb/26cb69eaa58afb9e7bccea75c57323fbe0850602.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/jmd.2011.5.593"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Bernoulli equilibrium states for surface diffeomorphisms

Omri M. Sarig
<span title="">2011</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ebeyl2om5vbsrbiuzncpyjustm" style="color: black;">Journal of Modern Dynamics</a> </i> &nbsp;
Suppose f : M → M is a C 1+α (α > 0) diffeomorphism on a compact smooth orientable manifold M of dimension two, and let µ Ψ be an equilibrium measure for a Hölder continuous potential Ψ : M → R.  ...  We show that if µ Ψ has positive metric entropy, then f is measure theoretically isomorphic mod µ Ψ to the product of a Bernoulli scheme and a finite rotation.  ...  This was extended by Bowen [B2] to all Axiom A diffeomorphisms, using Parry's characterization of the measure of maximal entropy for a subshift of finite type [Pa] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/jmd.2011.5.525">doi:10.3934/jmd.2011.5.525</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kwjgqmkkzng5riuasxm6csignm">fatcat:kwjgqmkkzng5riuasxm6csignm</a> </span>
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Bernoulli equilibrium states for surface diffeomorphisms [article]

Omri Sarig
<span title="2011-07-19">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Suppose f is a C^1+α surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential.  ...  We show that if m has positive metric entropy, then f is measure theoretically isomorphic to the product of a Bernoulli scheme and a finite rotation.  ...  This was extended by Bowen [B2] to all Axiom A diffeomorphisms, using Parry's characterization of the measure of maximal entropy for a subshift of finite type [Pa] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1107.3711v1">arXiv:1107.3711v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sepyesutavbjjlpkbcgmlukome">fatcat:sepyesutavbjjlpkbcgmlukome</a> </span>
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The ergodic theory of AxiomA flows

Rufus Bowen, David Ruelle
<span title="">1975</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/of2b2q3emjhk7dpzwv2fcyfhpa" style="color: black;">Inventiones Mathematicae</a> </i> &nbsp;
1% is an equilibrium state for qo.  ...  So #' is an equilibrium state for ~o*,/~'=#e, and p=p~. Thus/~,~ is the unique equilibrium state.  ...  Appendix Throughout what follows A will be a hyperbolic set for the C r flow (ft) on the manifold M (r> 1). We recall that, by assumption, the Riemann metric on M is adapted to fl (see Introduction).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01389848">doi:10.1007/bf01389848</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lufymcnn2vdnxppvf6uxt4epqm">fatcat:lufymcnn2vdnxppvf6uxt4epqm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160804121213/http://www.ihes.fr:80/~ruelle/PUBLICATIONS/[42].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/d6/55/d6556552811c9cb2e88252bbb3012e06c2e60fa5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01389848"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 541 of Mathematical Reviews Vol. 54, Issue 2 [page]

<span title="">1977</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 under review establishes the inequality for an Axiom A no-cycle diffeomorphism by means of an induction argument and a local version of the inequality for a basic set.  ...  diffeomorphism of a compact manifold M and let Q be a connected Axiom A attractor (i.e., Q is a closed connected subset of M, fQ=Q, the periodic points of f|Q are dense in Q, Q is a hyperbolic set, and  ... 
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Symbolic Dynamics for Hyperbolic Flows

Rufus Bowen
<span title="">1973</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkzouzjw7zaljamw6gqar2a3di" style="color: black;">American Journal of Mathematics</a> </i> &nbsp;
For A an « x n matrix of 0's and l's, the set 2 A = {xe2": A X/tXj+l = 1 for all i) is compact and tf-invariant. A basic hyperbolic set A will be closely related to a certain symbolic space I A .  ...  the one-dimensional bundle tangent to the flow, and there are constants c, X > 0 so that there is an open set U 3 A with A = fi' e */< ^ Basic hyperbolic sets occur in Smale's Axiom A flows [11], a class  ...  We remark that Sinai [10] used the slightly different formalism of Gibbs state. If f t \A is topologically mixing, then the measure fx+ is Bernoulli.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2373793">doi:10.2307/2373793</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wpjc72gtsnfcpkl5ftzldz2lni">fatcat:wpjc72gtsnfcpkl5ftzldz2lni</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922234611/http://www.mathunion.org/ICM/ICM1974.2/Main/icm1974.2.0299.0302.ocr.pdf?origin%3Dpublication_detail" 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/3b/02/3b020429a471a083c1bd8c5fe3403077743dbd07.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2373793"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Geometrical constructions of equilibrium states

Pablo D. Carrasco, Federico Rodriguez-Hertz
<span title="2021-09-09">2021</span> <i title="Cellule MathDoc/CEDRAM"> Mathematics Research Reports </i> &nbsp;
We also establish very fine statistical properties (Bernoulliness), and we give a characterization of equilibrium states in terms of their conditional measures in the stable/unstable lamination, similar  ...  For such systems, we give in particular a constructive proof of the existence of the SRB measure and of the entropy maximizing measure.  ...  constructions of equilibrium states  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5802/mrr.9">doi:10.5802/mrr.9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mn3stc57vjhrnhhzd65ci6kira">fatcat:mn3stc57vjhrnhhzd65ci6kira</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210914222725/https://mrr.centre-mersenne.org/item/10.5802/mrr.9.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/c7/cf/c7cfcabf1fb038ad79613dd33308b0ef27df8e82.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5802/mrr.9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 2087 of Mathematical Reviews Vol. , Issue 82e [page]

<span title="">1982</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 proof is carried out only for the case of the discrete flow generated by a baker’s transformation but the proof for a general Bernoulli system is stated to be similar.  ...  A consequence was that neither Q-stability nor Axiom A are C’-generic (r>2) for flows on any surface.  ... 
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Equilibrium measures, prehistories distributions and fractal dimensions for endomorphisms

Eugen Mihailescu
<span title="">2012</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rcpeuakxozcbxkr5eegcbenv4q" style="color: black;">Discrete and Continuous Dynamical Systems. Series A</a> </i> &nbsp;
These limit measures are in many cases shown to be equal to certain equilibrium measures for Hölder potentials.  ...  We study then the 1-sided Bernoullicity (or lack of it) for certain measures invariant to endomorphisms, and give a Classification Theorem for the ergodic and metric types of behaviour of perturbations  ...  sided Bernoulli shifts, for various equilibrium measures of the non-invertible system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/dcds.2012.32.2485">doi:10.3934/dcds.2012.32.2485</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/stn62cviy5dkxjwzwe4rffottm">fatcat:stn62cviy5dkxjwzwe4rffottm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809035606/http://www.imar.ro/~mihailes/DCDS-feb12-final.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/e0/ff/e0ffc5971c808665bfd40fdd9c4d63494f0f07c8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/dcds.2012.32.2485"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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