Conformal Fractals :: Ergodic Theory Methods.
"This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2010.
|
| Schriftenreihe: | London Mathematical Society lecture note series.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research"--Provided by publisher |
| Beschreibung: | 1 online resource (366 pages) |
| Bibliographie: | Includes bibliographical references (pages 336-348) and index. |
| ISBN: | 9781107094635 1107094631 9781107088450 1107088453 9781139193184 113919318X |
Internformat
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| 505 | 0 | 0 | |t Introduction -- |g 1. |t Basic examples and definitions -- |g 2. Measure-preserving endomorphisms -- |g 3. |t Ergodic theory on compact metric spaces -- |g 4. |t Distance-expanding maps -- |g 5. |t Thermodynamical formalism -- |g 6. |t Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- |g 7. |t Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- |g 8. |t Fractal dimensions -- |g 9. |t Conformal expanding repellers -- |g 10. |t Sullivan's classification of conformal expanding repellers -- |g 11. |t Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- |g 12. |t Conformal measures. |
| 520 | |a "This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research"--Provided by publisher | ||
| 650 | 0 | |a Conformal geometry. |0 http://id.loc.gov/authorities/subjects/sh89002613 | |
| 650 | 0 | |a Ergodic theory. |0 http://id.loc.gov/authorities/subjects/sh85044600 | |
| 650 | 0 | |a Fractals. |0 http://id.loc.gov/authorities/subjects/sh85051147 | |
| 650 | 0 | |a Iterative methods (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85069058 | |
| 650 | 6 | |a Géométrie conforme. | |
| 650 | 6 | |a Théorie ergodique. | |
| 650 | 6 | |a Fractales. | |
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| 650 | 7 | |a Iterative methods (Mathematics) |2 fast | |
| 655 | 0 | |a Electronic books. | |
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| contents | Introduction -- Basic examples and definitions -- Ergodic theory on compact metric spaces -- Distance-expanding maps -- Thermodynamical formalism -- Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- Fractal dimensions -- Conformal expanding repellers -- Sullivan's classification of conformal expanding repellers -- Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- Conformal measures. |
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| indexdate | 2024-11-27T13:25:24Z |
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| isbn | 9781107094635 1107094631 9781107088450 1107088453 9781139193184 113919318X |
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| series | London Mathematical Society lecture note series. |
| series2 | London Mathematical Society Lecture Note Series ; |
| spelling | Przytycki, Feliks. Conformal Fractals : Ergodic Theory Methods. Cambridge : Cambridge University Press, 2010. 1 online resource (366 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Lecture Note Series ; v. 371 Print version record. Includes bibliographical references (pages 336-348) and index. Introduction -- 1. Basic examples and definitions -- 2. Measure-preserving endomorphisms -- 3. Ergodic theory on compact metric spaces -- 4. Distance-expanding maps -- 5. Thermodynamical formalism -- 6. Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- 7. Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- 8. Fractal dimensions -- 9. Conformal expanding repellers -- 10. Sullivan's classification of conformal expanding repellers -- 11. Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- 12. Conformal measures. "This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research"--Provided by publisher Conformal geometry. http://id.loc.gov/authorities/subjects/sh89002613 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Fractals. http://id.loc.gov/authorities/subjects/sh85051147 Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Géométrie conforme. Théorie ergodique. Fractales. Itération (Mathématiques) fractals. aat MATHEMATICS Topology. bisacsh Conformal geometry fast Ergodic theory fast Fractals fast Iterative methods (Mathematics) fast Electronic books. Urbanski, Mariusz. has work: Conformal fractals (Text) https://id.oclc.org/worldcat/entity/E39PCH46xGKYXTBjM7dCDBtdwC https://id.oclc.org/worldcat/ontology/hasWork Print version: Przytycki, Feliks. Conformal Fractals : Ergodic Theory Methods. Cambridge : Cambridge University Press, ©2010 9780521438001 London Mathematical Society lecture note series. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570406 Volltext |
| spellingShingle | Przytycki, Feliks Conformal Fractals : Ergodic Theory Methods. London Mathematical Society lecture note series. Introduction -- Basic examples and definitions -- Ergodic theory on compact metric spaces -- Distance-expanding maps -- Thermodynamical formalism -- Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- Fractal dimensions -- Conformal expanding repellers -- Sullivan's classification of conformal expanding repellers -- Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- Conformal measures. Conformal geometry. http://id.loc.gov/authorities/subjects/sh89002613 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Fractals. http://id.loc.gov/authorities/subjects/sh85051147 Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Géométrie conforme. Théorie ergodique. Fractales. Itération (Mathématiques) fractals. aat MATHEMATICS Topology. bisacsh Conformal geometry fast Ergodic theory fast Fractals fast Iterative methods (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh89002613 http://id.loc.gov/authorities/subjects/sh85044600 http://id.loc.gov/authorities/subjects/sh85051147 http://id.loc.gov/authorities/subjects/sh85069058 |
| title | Conformal Fractals : Ergodic Theory Methods. |
| title_alt | Introduction -- Basic examples and definitions -- Ergodic theory on compact metric spaces -- Distance-expanding maps -- Thermodynamical formalism -- Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- Fractal dimensions -- Conformal expanding repellers -- Sullivan's classification of conformal expanding repellers -- Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- Conformal measures. |
| title_auth | Conformal Fractals : Ergodic Theory Methods. |
| title_exact_search | Conformal Fractals : Ergodic Theory Methods. |
| title_full | Conformal Fractals : Ergodic Theory Methods. |
| title_fullStr | Conformal Fractals : Ergodic Theory Methods. |
| title_full_unstemmed | Conformal Fractals : Ergodic Theory Methods. |
| title_short | Conformal Fractals : |
| title_sort | conformal fractals ergodic theory methods |
| title_sub | Ergodic Theory Methods. |
| topic | Conformal geometry. http://id.loc.gov/authorities/subjects/sh89002613 Ergodic theory. http://id.loc.gov/authorities/subjects/sh85044600 Fractals. http://id.loc.gov/authorities/subjects/sh85051147 Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Géométrie conforme. Théorie ergodique. Fractales. Itération (Mathématiques) fractals. aat MATHEMATICS Topology. bisacsh Conformal geometry fast Ergodic theory fast Fractals fast Iterative methods (Mathematics) fast |
| topic_facet | Conformal geometry. Ergodic theory. Fractals. Iterative methods (Mathematics) Géométrie conforme. Théorie ergodique. Fractales. Itération (Mathématiques) fractals. MATHEMATICS Topology. Conformal geometry Ergodic theory Fractals Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570406 |
| work_keys_str_mv | AT przytyckifeliks conformalfractalsergodictheorymethods AT urbanskimariusz conformalfractalsergodictheorymethods |