Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / / Mariusz Urbański, Mario Roy, Sara Munday.
The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, e...
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Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2021] ©2022 |
Year of Publication: | 2021 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
69/1 |
Online Access: | |
Physical Description: | 1 online resource (XXVIII, 430 p.) |
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050 | 4 | |a QA611.5 |b .U73 2022 | |
072 | 7 | |a MAT007000 |2 bisacsh | |
082 | 0 | 4 | |a 515.48 |2 23 |
100 | 1 | |a Urbański, Mariusz, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / |c Mariusz Urbański, Mario Roy, Sara Munday. |
264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2021] | |
264 | 4 | |c ©2022 | |
300 | |a 1 online resource (XXVIII, 430 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a De Gruyter Expositions in Mathematics , |x 0938-6572 ; |v 69/1 | |
505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t List of Figures -- |t Introduction to Volume 1 -- |t Contents -- |t 1 Dynamical systems -- |t 2 Homeomorphisms of the circle -- |t 3 Symbolic dynamics -- |t 4 Distance expanding maps -- |t 5 (Positively) expansive maps -- |t 6 Shub expanding endomorphisms -- |t 7 Topological entropy -- |t 8 Ergodic theory -- |t 9 Measure-theoretic entropy -- |t 10 Infinite invariant measures -- |t 11 Topological pressure -- |t 12 The variational principle and equilibrium states -- |t Appendix A. A selection of classical results -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Mai 2023) | |
650 | 0 | |a Ergodic theory. | |
650 | 4 | |a Dynamisches System. | |
650 | 4 | |a Ergodentheorie. | |
650 | 4 | |a Fraktal. | |
650 | 7 | |a MATHEMATICS / Differential Equations / General. |2 bisacsh | |
700 | 1 | |a Munday, Sara, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
700 | 1 | |a Roy, Mario, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Plus DeG Package 2022 Part 1 |z 9783110766820 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2021 English |z 9783110754001 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2021 |z 9783110753776 |o ZDB-23-DGG |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2021 English |z 9783110754131 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2021 |z 9783110753905 |o ZDB-23-DMA |
776 | 0 | |c EPUB |z 9783110702750 | |
776 | 0 | |c print |z 9783110702644 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9783110702682 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9783110702682 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9783110702682/original |
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