Graph directed Markov systems: geometry and dynamics of limit sets
The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of confo...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
|
| Schriftenreihe: | Cambridge tracts in mathematics
148 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students |
| Beschreibung: | 1 Online-Ressource (xi, 281 Seiten) |
| ISBN: | 9780511543050 |
| DOI: | 10.1017/CBO9780511543050 |
Internformat
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| 100 | 1 | |a Mauldin, Richard Daniel |d 1943- |e Verfasser |0 (DE-588)12837389X |4 aut | |
| 245 | 1 | 0 | |a Graph directed Markov systems |b geometry and dynamics of limit sets |c R. Daniel Mauldin and Mariusz Urbaʹnski |
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| 490 | 0 | |a Cambridge tracts in mathematics |v 148 | |
| 505 | 8 | |a Introduction -- 1. Preliminaries -- 2. Symbolic dynamics -- 3. Hḻder families of functions -- 4. Conformal graph directed Markov systems -- 5. Examples of graph directed Markov systems -- 6. Conformal iterated function systems -- 7. Dynamical rigidity of conformal iterated function systems -- 8. Parabolic iterated function systems -- 9. Parabolic systems: Hausdorff and packing measures | |
| 520 | |a The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students | ||
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Geometric function theory | |
| 650 | 4 | |a Limit theorems (Probability theory) | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Mauldin, Richard Daniel 1943- |
| author_GND | (DE-588)12837389X |
| author_facet | Mauldin, Richard Daniel 1943- |
| author_role | aut |
| author_sort | Mauldin, Richard Daniel 1943- |
| author_variant | r d m rd rdm |
| building | Verbundindex |
| bvnumber | BV043942215 |
| classification_rvk | SK 820 SK 890 |
| collection | ZDB-20-CBO |
| contents | Introduction -- 1. Preliminaries -- 2. Symbolic dynamics -- 3. Hḻder families of functions -- 4. Conformal graph directed Markov systems -- 5. Examples of graph directed Markov systems -- 6. Conformal iterated function systems -- 7. Dynamical rigidity of conformal iterated function systems -- 8. Parabolic iterated function systems -- 9. Parabolic systems: Hausdorff and packing measures |
| ctrlnum | (ZDB-20-CBO)CR9780511543050 (OCoLC)850573870 (DE-599)BVBBV043942215 |
| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543050 |
| format | Electronic eBook |
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| id | DE-604.BV043942215 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511543050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351184 |
| oclc_num | 850573870 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xi, 281 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
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| publisher | Cambridge University Press |
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| spelling | Mauldin, Richard Daniel 1943- Verfasser (DE-588)12837389X aut Graph directed Markov systems geometry and dynamics of limit sets R. Daniel Mauldin and Mariusz Urbaʹnski Cambridge Cambridge University Press 2003 1 Online-Ressource (xi, 281 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 148 Introduction -- 1. Preliminaries -- 2. Symbolic dynamics -- 3. Hḻder families of functions -- 4. Conformal graph directed Markov systems -- 5. Examples of graph directed Markov systems -- 6. Conformal iterated function systems -- 7. Dynamical rigidity of conformal iterated function systems -- 8. Parabolic iterated function systems -- 9. Parabolic systems: Hausdorff and packing measures The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students Markov processes Graph theory Geometric function theory Limit theorems (Probability theory) Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Markov-Prozess (DE-588)4134948-9 s Geometrische Funktionentheorie (DE-588)4156711-0 s Grenzwertsatz (DE-588)4158163-5 s Urbański, Mariusz Sonstige oth Erscheint auch als Druck-Ausgabe 978-0-521-82538-2 https://doi.org/10.1017/CBO9780511543050 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mauldin, Richard Daniel 1943- Graph directed Markov systems geometry and dynamics of limit sets Introduction -- 1. Preliminaries -- 2. Symbolic dynamics -- 3. Hḻder families of functions -- 4. Conformal graph directed Markov systems -- 5. Examples of graph directed Markov systems -- 6. Conformal iterated function systems -- 7. Dynamical rigidity of conformal iterated function systems -- 8. Parabolic iterated function systems -- 9. Parabolic systems: Hausdorff and packing measures Markov processes Graph theory Geometric function theory Limit theorems (Probability theory) Markov-Prozess (DE-588)4134948-9 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd Graphentheorie (DE-588)4113782-6 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4156711-0 (DE-588)4113782-6 (DE-588)4158163-5 |
| title | Graph directed Markov systems geometry and dynamics of limit sets |
| title_auth | Graph directed Markov systems geometry and dynamics of limit sets |
| title_exact_search | Graph directed Markov systems geometry and dynamics of limit sets |
| title_full | Graph directed Markov systems geometry and dynamics of limit sets R. Daniel Mauldin and Mariusz Urbaʹnski |
| title_fullStr | Graph directed Markov systems geometry and dynamics of limit sets R. Daniel Mauldin and Mariusz Urbaʹnski |
| title_full_unstemmed | Graph directed Markov systems geometry and dynamics of limit sets R. Daniel Mauldin and Mariusz Urbaʹnski |
| title_short | Graph directed Markov systems |
| title_sort | graph directed markov systems geometry and dynamics of limit sets |
| title_sub | geometry and dynamics of limit sets |
| topic | Markov processes Graph theory Geometric function theory Limit theorems (Probability theory) Markov-Prozess (DE-588)4134948-9 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd Graphentheorie (DE-588)4113782-6 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Markov processes Graph theory Geometric function theory Limit theorems (Probability theory) Markov-Prozess Geometrische Funktionentheorie Graphentheorie Grenzwertsatz |
| url | https://doi.org/10.1017/CBO9780511543050 |
| work_keys_str_mv | AT mauldinricharddaniel graphdirectedmarkovsystemsgeometryanddynamicsoflimitsets AT urbanskimariusz graphdirectedmarkovsystemsgeometryanddynamicsoflimitsets |