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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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2021] ©2022 |
Year of Publication: | 2021 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
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Physical Description: | 1 online resource (XXVIII, 430 p.) |
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Urbański, Mariusz, author. aut http://id.loc.gov/vocabulary/relators/aut Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / Mariusz Urbański, Mario Roy, Sara Munday. Berlin ; Boston : De Gruyter, [2021] ©2022 1 online resource (XXVIII, 430 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 69/1 Frontmatter -- Preface -- List of Figures -- Introduction to Volume 1 -- Contents -- 1 Dynamical systems -- 2 Homeomorphisms of the circle -- 3 Symbolic dynamics -- 4 Distance expanding maps -- 5 (Positively) expansive maps -- 6 Shub expanding endomorphisms -- 7 Topological entropy -- 8 Ergodic theory -- 9 Measure-theoretic entropy -- 10 Infinite invariant measures -- 11 Topological pressure -- 12 The variational principle and equilibrium states -- Appendix A. A selection of classical results -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Mai 2023) Ergodic theory. Dynamisches System. Ergodentheorie. Fraktal. MATHEMATICS / Differential Equations / General. bisacsh Munday, Sara, author. aut http://id.loc.gov/vocabulary/relators/aut Roy, Mario, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 9783110766820 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English 9783110754001 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 9783110753776 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 English 9783110754131 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 9783110753905 ZDB-23-DMA EPUB 9783110702750 print 9783110702644 https://doi.org/10.1515/9783110702682 https://www.degruyter.com/isbn/9783110702682 Cover https://www.degruyter.com/document/cover/isbn/9783110702682/original |
language |
English |
format |
eBook |
author |
Urbański, Mariusz, Urbański, Mariusz, Munday, Sara, Roy, Mario, |
spellingShingle |
Urbański, Mariusz, Urbański, Mariusz, Munday, Sara, Roy, Mario, Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / De Gruyter Expositions in Mathematics , Frontmatter -- Preface -- List of Figures -- Introduction to Volume 1 -- Contents -- 1 Dynamical systems -- 2 Homeomorphisms of the circle -- 3 Symbolic dynamics -- 4 Distance expanding maps -- 5 (Positively) expansive maps -- 6 Shub expanding endomorphisms -- 7 Topological entropy -- 8 Ergodic theory -- 9 Measure-theoretic entropy -- 10 Infinite invariant measures -- 11 Topological pressure -- 12 The variational principle and equilibrium states -- Appendix A. A selection of classical results -- Bibliography -- Index |
author_facet |
Urbański, Mariusz, Urbański, Mariusz, Munday, Sara, Roy, Mario, Munday, Sara, Munday, Sara, Roy, Mario, Roy, Mario, |
author_variant |
m u mu m u mu s m sm m r mr |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Munday, Sara, Munday, Sara, Roy, Mario, Roy, Mario, |
author2_variant |
s m sm m r mr |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Urbański, Mariusz, |
title |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / |
title_full |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / Mariusz Urbański, Mario Roy, Sara Munday. |
title_fullStr |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / Mariusz Urbański, Mario Roy, Sara Munday. |
title_full_unstemmed |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / Mariusz Urbański, Mario Roy, Sara Munday. |
title_auth |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / |
title_alt |
Frontmatter -- Preface -- List of Figures -- Introduction to Volume 1 -- Contents -- 1 Dynamical systems -- 2 Homeomorphisms of the circle -- 3 Symbolic dynamics -- 4 Distance expanding maps -- 5 (Positively) expansive maps -- 6 Shub expanding endomorphisms -- 7 Topological entropy -- 8 Ergodic theory -- 9 Measure-theoretic entropy -- 10 Infinite invariant measures -- 11 Topological pressure -- 12 The variational principle and equilibrium states -- Appendix A. A selection of classical results -- Bibliography -- Index |
title_new |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / |
title_sort |
non-invertible dynamical systems. ergodic theory – finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps / |
series |
De Gruyter Expositions in Mathematics , |
series2 |
De Gruyter Expositions in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2021 |
physical |
1 online resource (XXVIII, 430 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- List of Figures -- Introduction to Volume 1 -- Contents -- 1 Dynamical systems -- 2 Homeomorphisms of the circle -- 3 Symbolic dynamics -- 4 Distance expanding maps -- 5 (Positively) expansive maps -- 6 Shub expanding endomorphisms -- 7 Topological entropy -- 8 Ergodic theory -- 9 Measure-theoretic entropy -- 10 Infinite invariant measures -- 11 Topological pressure -- 12 The variational principle and equilibrium states -- Appendix A. A selection of classical results -- Bibliography -- Index |
isbn |
9783110702682 9783110766820 9783110754001 9783110753776 9783110754131 9783110753905 9783110702750 9783110702644 |
issn |
0938-6572 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA611 |
callnumber-sort |
QA 3611.5 U73 42022 |
url |
https://doi.org/10.1515/9783110702682 https://www.degruyter.com/isbn/9783110702682 https://www.degruyter.com/document/cover/isbn/9783110702682/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.48 |
dewey-sort |
3515.48 |
dewey-raw |
515.48 |
dewey-search |
515.48 |
doi_str_mv |
10.1515/9783110702682 |
oclc_num |
1286806634 |
work_keys_str_mv |
AT urbanskimariusz noninvertibledynamicalsystemsergodictheoryfiniteandinfinitethermodynamicformalismsymbolicdynamicsanddistanceexpandingmaps AT mundaysara noninvertibledynamicalsystemsergodictheoryfiniteandinfinitethermodynamicformalismsymbolicdynamicsanddistanceexpandingmaps AT roymario noninvertibledynamicalsystemsergodictheoryfiniteandinfinitethermodynamicformalismsymbolicdynamicsanddistanceexpandingmaps |
status_str |
n |
ids_txt_mv |
(DE-B1597)549663 (OCoLC)1286806634 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2021 |
is_hierarchy_title |
Non-Invertible Dynamical Systems. Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1 |
author2_original_writing_str_mv |
noLinkedField noLinkedField noLinkedField noLinkedField |
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fullrecord |
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