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Approximation in ergodic theory, Borel, and Cantor dynamics [article]

S. Bezuglyi, J. Kwiatkowski, K. Medynets
2005 arXiv   pre-print
This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics.  ...  Various topological properties (density, connectedness, genericity) of these groups and their subsets (subgroups) are studied.  ...  In this paper, we intend to present a unified approach to the study of topological properties of transformation groups arisen in ergodic theory, Borel, and Cantor dynamics.  ... 
arXiv:math/0504490v1 fatcat:2dnop6ajyfgttms6nndprgnjma

Integer Cantor sets and an order-two ergodic theorem

Albert M. Fisher
1993 Ergodic Theory and Dynamical Systems  
the right-hand order-two density of the middle-third Cantor set.  ...  (all zeroes)... 101000101000000000101 ... corresponding to the integer Cantor set [C] = { £ " 0 a,3': a<=0 or 2, NeN}.  ...  We wish to thank Jon Aaronson, Tim Bedford, Mariusz Urbanski, Michel Dekking and Manfred Denker for discussions, and Dan Rudolph for supplying a key observation: that the base of the tower could be coded  ... 
doi:10.1017/s0143385700007197 fatcat:r4ilsmfahzfo7mtb5yzzexzwn4

Graph Theoretic Structure of Maps of the Cantor Space [article]

Nilson C. Bernardes Jr., Udayan B. Darji
2012 arXiv   pre-print
Our analogous investigation in the space of continuous self-maps of the Cantor space yields a surprising result: there is a comeager subset of the space of self-maps of the Cantor space such that any two  ...  In this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of the space of homeomorphisms and the space of self-maps of the Cantor space.  ...  The second author thanks the Mathematics Institute of Federal University of Rio de Janeiro for its support and hospitality during his one-month visit in 2011.  ... 
arXiv:1205.4155v1 fatcat:rwbj5twuwvh2ljehvtnocl4jna

Asymptotic mapping class groups of Cantor manifolds and their finiteness properties [article]

Javier Aramayona, Kai-Uwe Bux, Jonas Flechsig, Nansen Petrosyan, Xiaolei Wu
2021 arXiv   pre-print
A Cantor manifold 𝒞 is a non-compact manifold obtained by gluing (holed) copies of a fixed compact manifold Y in a tree-like manner.  ...  Generalizing classical families of groups due to Brin, Dehornoy, and Funar- Kapoudjian, we introduce the asymptotic mapping class group ℬ of 𝒞, whose elements are proper isotopy classes of self-diffeomorphisms  ...  In turn this boils down, using a well-known argument in discrete Morse theory, to analyze the connectivity of the descending links; we refer the reader to Appendix A.1 for a discussion on this.  ... 
arXiv:2110.05318v2 fatcat:dd6yvkwc3veppm3kwg76lkirwu

Graph theoretic structure of maps of the Cantor space

Nilson C. Bernardes, Udayan B. Darji
2012 Advances in Mathematics  
In this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of spaces H({0, 1} N ) and C({0, 1} N ), the space of homeomorphisms and the space of self-maps of the  ...  Cantor space, respectively.  ...  The second author thanks the Mathematics Institute of Federal University of Rio de Janeiro for its support and hospitality during his one-month visit in 2011.  ... 
doi:10.1016/j.aim.2012.05.024 fatcat:6ohccionfjbwtjqanmmvlgll4a

Rigidity properties of full groups of pseudogroups over the Cantor set [article]

Nicolás Matte Bon
2018 arXiv   pre-print
shifts of finite type), full groups of minimal Z-actions on the Cantor set, and a class of groups of interval exchanges.  ...  We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature.  ...  I am grateful to Alessandro Sisto for pointing out a property of asymptotic dimension (Proposition 2.5) which allowed me to improve the statement of Corollary 1.6.  ... 
arXiv:1801.10133v2 fatcat:k6fnol5rcjhezlslryky6pqquq

Spectral triples for AF C*-algebras and metrics on the Cantor set [article]

Cristina Antonescu, Erik Christensen
2004 arXiv   pre-print
lead to an, apparently, new way of constructing a representative for a Cantor set of any given Hausdorff dimension.  ...  In the particular case of a UHF C*-algebra, the construction can be made in a way, which relates directly to the dimensions of the increasing sequence of subalgebras.The algebra of continuous functions  ...  Having this, we searched the literature for a unified representation theory for Cantor sets of any positive dimension. We have not found a general theory, but we found some examples [FY] , [Ke] .  ... 
arXiv:math/0309044v2 fatcat:zsctdobum5ac7habfxgndjznh4

Page 5140 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
|Mazzanti, Stefano] (I-UDIN-MI-; Udine Cantor diagrams: a unifying discussion of self-reference. (English summary) Appl. Categ. Structures 11 (2003), no. 4, 313-336.  ...  Summary: “Within the framework of category theory, Cantor diagrams are introduced as the common structure of the self- reference constructions by Cantor, Russell, Richard, Gédel, Péter, Turing, Kleene,  ... 

Zipf's law, 1/f noise, and fractal hierarchy

Yanguang Chen
2011 Chaos, Solitons & Fractals  
set of references developed within the specific scientific domains.  ...  The self-similar hierarchy is a more general framework or structure which can be used to encompass or unify different scaling phenomena and rules in both physical and social systems such as cities, rivers  ...  Acknowledgements: This research was sponsored by the National Natural Science Foundation of China (https://isis.nsfc.gov.cn/portal/index.asp。 Grant No. 40771061).  ... 
doi:10.1016/j.chaos.2011.10.001 fatcat:nsypxa4ff5fnxorhyb2aurswym

A Provably Correct Compiler Generator

Jens Palsberg
1992 DAIMI Report Series  
We have designed, implemented, and proved the correctness of a compiler generator that accepts action semantic descriptions of imperative programming languages.  ...  The author thanks Peter Mosses, Michael Schwartzbach, and the referees for helpful comments on a draft of the paper. The author also thanks Peter Ørbaek for implementing the Cantor system.  ...  We also discuss why we do not treat recursion.  ... 
doi:10.7146/dpb.v21i382.6614 fatcat:3oqtebreffcfzaijz7dfitzczu

A provably correct compiler generator [chapter]

Jens Palsberg
1992 Lecture Notes in Computer Science  
We have designed, implemented, and proved the correctness of a compiler generator that accepts action semantic descriptions of imperative programming languages.  ...  We also discuss why we do not treat recursion.  ...  The specification and proof of correctness of the Cantor system is an experiment in using the framework of unified algebras, developed by Mosses [35, 33, 34] .  ... 
doi:10.1007/3-540-55253-7_25 fatcat:z2ff2ya675aijntr6z7rmgwhie

Fractal nature of material microstructure and size effects on apparent mechanical properties

Alberto Carpinteri
1994 Mechanics of materials (Print)  
The problems of the size effects on tensile strength and fracture energy of brittle and disordered materials (concrete, rocks, ceramics, etc.) are reconsidered under a new and unifying light cast on by  ...  Anaìogously, in the case of fracture energy, the dimensional increment represents self-similar tortuosity of the fracture surface, as well as self-similar overlapping and distribution of microcracks in  ...  Acknowledgements The present research was carried out with the financial support of the Ministry of University and Scientific Research (MURST) and the National Research Council (CNR).  ... 
doi:10.1016/0167-6636(94)00008-5 fatcat:3qttjpzm6bbbth7tog7wy77ilq

Resonance and Fractal Geometry

Henk W. Broer
2012 Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications  
This paper gives a summary of the background theory, veined by examples.  ...  The latter phenomena occur for parameter values in fractal sets of positive measure. We describe a universal phenomenon that plays an important role in modelling.  ...  Acknowledgements The author thanks Konstantinos Efstathiou, Aernout van Enter and Ferdinand Verhulst for their help in the preparation of this paper.  ... 
doi:10.1007/s10440-012-9670-x fatcat:2eksvsuytjegllcv42dev7btme

An Ideal Convergence

Konrad Aguilar, Samantha Brooker, Frédéric Latrémolière, Alejandra López
2021 Notices of the American Mathematical Society  
The first author is grateful to IMADA at Syddansk Universitet, where some of this work was completed, and gratefully acknowledges the financial support from the Independent Research Fund Denmark through  ...  We will discuss this and ideals of C*-algebras more later, but now, we present the construction of from a Bratteli diagram. Example 3.3.  ...  Let be a C*-algebra. If ⊆ is a norm-closed two-sided ideal of , then is self-adjoint and thus a C*-subalgebra of .  ... 
doi:10.1090/noti2338 fatcat:bgv2js2kqjfulpaoqv6uwrzblu

Rapid Beam Forming in Smart Antennas Using Smart-Fractal Concepts Employing Combinational Approach Algorithms

Mounissamy Levy, Sumanta Bose, D. Sriram Kumar, Anh Van Dinh
2012 International Journal of Antennas and Propagation  
Smart antennas use an array of low gain antenna elements which are connected by a network. Fractal concepts have been used in antenna arrays recently.  ...  Smart antennas offer a broad range of ways to improve wireless system performance. They provide enhanced coverage through range extension, hole filling, and better building penetration.  ...  [6] demonstrated that the diffracted field of a self-similar fractal screen also exhibits self-similarity.  ... 
doi:10.1155/2012/467492 fatcat:dahtdc6c5fahzh2etjldymvfxm
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