Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps:
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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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2022]
|
| Series: | De Gruyter expositions in mathematics
volume 69/1 |
| Subjects: | |
| Online Access: | DE-1043 DE-1046 DE-858 DE-898 DE-859 DE-860 DE-91 DE-20 DE-706 DE-739 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (XXVII, 427 Seiten) |
| ISBN: | 9783110702682 9783110702750 |
| DOI: | 10.1515/9783110702682 |
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| author | Urbański, Mariusz 1958- Roy, Mario 1972- Munday, Sara |
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| spelling | Urbański, Mariusz 1958- Verfasser (DE-588)120432684 aut Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps Mariusz Urbański, Mario Roy, Sara Munday Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps Berlin ; Boston De Gruyter [2022] © 2022 1 Online-Ressource (XXVII, 427 Seiten) txt rdacontent c rdamedia cr rdacarrier De Gruyter expositions in mathematics volume 69/1 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 Dynamisches System Ergodentheorie Fraktal MATHEMATICS / Differential Equations / General bisacsh Roy, Mario 1972- Verfasser (DE-588)122810333 aut Munday, Sara Verfasser (DE-588)1116447908 aut Erscheint auch als Druck-Ausgabe 978-3-11-070264-4 De Gruyter expositions in mathematics volume 69/1 (DE-604)BV044998893 69,1 https://doi.org/10.1515/9783110702682 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Urbański, Mariusz 1958- Roy, Mario 1972- Munday, Sara Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps De Gruyter expositions in mathematics Dynamisches System Ergodentheorie Fraktal MATHEMATICS / Differential Equations / General bisacsh |
| title | Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps |
| title_alt | Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps |
| title_auth | Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps |
| title_exact_search | Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps |
| title_exact_search_txtP | Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps |
| title_full | Non-invertible dynamical systems. Volume 1, 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. Volume 1, 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. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps Mariusz Urbański, Mario Roy, Sara Munday |
| title_short | Non-invertible dynamical systems. Volume 1, Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps |
| title_sort | non invertible dynamical systems volume 1 ergodic theory finite and infinite thermodynamic formalism symbolic dynamics and distance expanding maps |
| topic | Dynamisches System Ergodentheorie Fraktal MATHEMATICS / Differential Equations / General bisacsh |
| topic_facet | Dynamisches System Ergodentheorie Fraktal MATHEMATICS / Differential Equations / General |
| url | https://doi.org/10.1515/9783110702682 |
| volume_link | (DE-604)BV044998893 |
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