Multifractal Analysis of Local Entropies for Expansive Homeomorphisms with Specification

Floris Takens, Evgeny Verbitski · Communications in Mathematical Physics · 1999

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Type: article
Published: 1999-06-01
Cited by: 89
References: 21
Access: Open access
DOI: https://doi.org/10.1007/s002200050627
OpenAlex: https://openalex.org/W2074428344
Semantic Scholar: https://api.semanticscholar.org/CorpusID:62815171

Keywords

Multifractal system, Pointwise, Expansive, Dynamical systems theory, Mathematics

References

Dimension theory in dynamical systemsYakov Pesin — 1997
Thermodynamic formalism. The mathematical structures of classical equilibrium statistical mechanics : Vol. 5. by David Ruelle, Addison Wesley, Reading, MA, 1978, $ 21.50F. Fer — 1980
Thermodynamics of chaotic systems : an introductionChristian Beck, Friedrich Schögl — 1993
Introduction to the Modern Theory of Dynamical SystemsJ.A. Zukas — 1998
Sets of “Non-typical” points have full topological entropy and full Hausdorff dimensionLuís Barreira, Jörg Schmeling — 2000
Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specificationNicolai Haydn, David Ruelle — 1992
TOPOLOGICAL ENTROPY FOR NONCOMPACT SETSRufus Bowen — 1973
Multifractal spectra and multifractal rigidity for horseshoesLuís Barreira, Ya. B. Pesin, J. Sehmeling — 1997
GENERALIZED ENTROPIES : RENYI AND CORRELATION INTEGRAL APPROACHFloris Takens, Evgeny Verbitski — 1998
On the completeness of multifractal spectraJörg Schmeling — 1999
Thermodynamic formalism for maps satisfying positive expan-siveness and speci cationDavid Ruelle — 1992
The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples.Yakov Pesin, Howard M. Weiss — 1997
DIMENSION THEORY IN DYNAMICAL SYSTEMS: CONTEMPORARY VIEWS AND APPLICATIONS By YAKOV B. PESIN Chicago Lectures in Mathematics, University of Chicago Press, 312 pp. Price: hardback 56, paperback 19.95. ISBN 0 226 66222 5Yakov Pesin — 1998
Differentiability properties of the pressure of a continuous transformation on a compact metric spacePeter Walters — 1992
Symbolic dynamics for β-shifts and self-normal numbersJörg Schmeling — 1997
Topological pressure and the variational principle for noncompact setsYa. B. Pesin, B. S. Pitskel’ — 1984
A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructionsYakov Pesin, Howard M. Weiss — 1997
On a general concept of multifractality: Multifractal spectra for dimensions, entropies, and Lyapunov exponents. Multifractal rigidity.Luís Barreira, Yakov Pesin, Jörg Schmeling — 1997
Introduction to Ergodic TheoryPeter Walters — 1977
Introduction to the modern theory of dynamical systemsKatok, Anatole, Hasselblatt, Boris — 1996

Cited by

Multifractal Analysis of Ergodic Averages: A Generalization of Eggleston's TheoremArkady Tempelman — 2001
Multifractal formalism derived from thermodynamicsVaughn Climenhaga — 2010
Multifractal Analysis of Dimensions and EntropiesFloris Takens, Evgeny Verbitski — 2000
Large deviations for empirical entropies of g-measuresJ-R Chazottes, Davide Gabrielli — 2004
Multifractal analysis of the irregular set for almost-additive sequences via large deviationsThiago Bomfim, Paulo Varandas — 2014
Systems with almost specification property may have zero entropyYiwei Dong — 2015
Multifractal analysis for weak Gibbs measures: from large deviations to irregular setsTHIAGO BOMFIM, PAULO VARANDAS — 2014
Irregular sets and conditional variational principles in dynamical systemsDaniel J. Thompson — 2009
Higher Multifractal Analysis for Simultaneous Actions of Fuchsian GroupsAlejandro Mesón, Fernando Vericat — 2007
An approach to the problem of phase transitions in the continuumAlejandro Mesón, Fernando Vericat — 2005
Multifractal Analysis for Gibbs Ground StatesAlejandro Mesón, Fernando Vericat — 2006
Multifractal Analysis for the Teichmüller FlowAlejandro Mesón, Fernando Vericat — 2012
Generalized fractal dimensions: equivalences and basic propertiesJean-Marie Barbaroux, François Germinet, Serguei Tcheremchantsev — 2001
A Note on Measure-Expansive DiffeomorphismsAlfonso Artigue, Dante Carrasco-Olivera — 2014
On the Statistical Distribution of First-Return Times of Balls and Cylinders in Chaotic SystemsG. MANTICA, S. VAIENTI — 2009
Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II: Non-linearity, divergence points and banach space valued spectraL. Olsen, Steffen Winter — 2007
On the uniqueness of Gibbs states in some dynamical systemsAlejandro Mesón, Fernando Vericat — 2009
Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averagesL. Olsen — 2003
Multifractal formalism derived from thermodynamics for general dynamical systemsVaughn Climenhaga — 2010
On the Kolmogorov-like generalization of Tsallis entropy, correlation entropies and multifractal analysisAlejandro Mesón, Fernando Vericat — 2002

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