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 holomorphi...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
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| Schriftenreihe: | London Mathematical Society lecture note series
371 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 354 pages) |
| ISBN: | 9781139193184 |
| DOI: | 10.1017/CBO9781139193184 |
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| 505 | 8 | 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 | ||
| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Fractals | |
| 650 | 4 | |a Ergodic theory | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
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| 700 | 1 | |a Urbański, Mariusz |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804176884718632960 |
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| any_adam_object | |
| author | Przytycki, Feliks |
| author_facet | Przytycki, Feliks |
| author_role | aut |
| author_sort | Przytycki, Feliks |
| author_variant | f p fp |
| building | Verbundindex |
| bvnumber | BV043942190 |
| classification_rvk | SI 320 |
| collection | ZDB-20-CBO |
| 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 |
| ctrlnum | (ZDB-20-CBO)CR9781139193184 (OCoLC)907963790 (DE-599)BVBBV043942190 |
| dewey-full | 514/.742 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.742 |
| dewey-search | 514/.742 |
| dewey-sort | 3514 3742 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139193184 |
| format | Electronic eBook |
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| id | DE-604.BV043942190 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139193184 |
| language | English |
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| oclc_num | 907963790 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 354 pages) |
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| publisher | Cambridge University Press |
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| spelling | Przytycki, Feliks Verfasser aut Conformal fractals ergodic theory methods Feliks Przytycki, Mariusz Urbański Cambridge Cambridge University Press 2010 1 online resource (x, 354 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 371 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Conformal geometry Fractals Ergodic theory Iterative methods (Mathematics) Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Fraktal (DE-588)4123220-3 s Ergodentheorie (DE-588)4015246-7 s Iteration (DE-588)4123457-1 s 1\p DE-604 Urbański, Mariusz Sonstige oth Erscheint auch als Druckausgabe 978-0-521-43800-1 https://doi.org/10.1017/CBO9781139193184 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Przytycki, Feliks Conformal fractals ergodic theory methods 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 Fractals Ergodic theory Iterative methods (Mathematics) Ergodentheorie (DE-588)4015246-7 gnd Fraktal (DE-588)4123220-3 gnd Iteration (DE-588)4123457-1 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4123220-3 (DE-588)4123457-1 |
| 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 Feliks Przytycki, Mariusz Urbański |
| title_fullStr | Conformal fractals ergodic theory methods Feliks Przytycki, Mariusz Urbański |
| title_full_unstemmed | Conformal fractals ergodic theory methods Feliks Przytycki, Mariusz Urbański |
| title_short | Conformal fractals |
| title_sort | conformal fractals ergodic theory methods |
| title_sub | ergodic theory methods |
| topic | Conformal geometry Fractals Ergodic theory Iterative methods (Mathematics) Ergodentheorie (DE-588)4015246-7 gnd Fraktal (DE-588)4123220-3 gnd Iteration (DE-588)4123457-1 gnd |
| topic_facet | Conformal geometry Fractals Ergodic theory Iterative methods (Mathematics) Ergodentheorie Fraktal Iteration |
| url | https://doi.org/10.1017/CBO9781139193184 |
| work_keys_str_mv | AT przytyckifeliks conformalfractalsergodictheorymethods AT urbanskimariusz conformalfractalsergodictheorymethods |