Typical dynamics of volume preserving homeomorphisms:
This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typic...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2000
|
| Schriftenreihe: | Cambridge tracts in mathematics
139 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley–Zehnder– Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property |
| Beschreibung: | 1 Online-Ressource (xix, 216 Seiten) |
| ISBN: | 9780511543180 |
| DOI: | 10.1017/CBO9780511543180 |
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| 505 | 8 | 0 | |t Volume preserving homeomorphisms of the cube |t Introduction to part I and II (compact manifolds) |t Measure preserving homeomorphisms |t Discrete approximations |t Transitive homeomorphisms of In and Rn |t Fixed points and area preservation |t Measure preserving lusin theorem |t Ergodic homeomorphisms |t Uniform approximation in g[In, delta] and generic properties in M[In, delta] |t Measure preserving homeomorphisms of a compact manifold |t Measures on compact manifolds |t Dynamics on compact manifolds |t Oeasure preserving homeomorphisms of a noncompact manifold |t Ergodic volume preserving homeomorphisms of Rn |t Manifolds where ergodicity is not generic |t Noncompact manifolds and ends |t Ergodic homeomorphisms: the results |t Ergodic homeomorphisms: proofs |t Other properties typical in M[X, u] |
| 520 | |a This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley–Zehnder– Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property | ||
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Datensatz im Suchindex
| _version_ | 1804176884605386752 |
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| any_adam_object | |
| author | Alpern, Steve 1948- |
| author_GND | (DE-588)143654365 (DE-588)172376777 |
| author_facet | Alpern, Steve 1948- |
| author_role | aut |
| author_sort | Alpern, Steve 1948- |
| author_variant | s a sa |
| building | Verbundindex |
| bvnumber | BV043942125 |
| classification_rvk | SK 350 |
| collection | ZDB-20-CBO |
| contents | Volume preserving homeomorphisms of the cube Introduction to part I and II (compact manifolds) Measure preserving homeomorphisms Discrete approximations Transitive homeomorphisms of In and Rn Fixed points and area preservation Measure preserving lusin theorem Ergodic homeomorphisms Uniform approximation in g[In, delta] and generic properties in M[In, delta] Measure preserving homeomorphisms of a compact manifold Measures on compact manifolds Dynamics on compact manifolds Oeasure preserving homeomorphisms of a noncompact manifold Ergodic volume preserving homeomorphisms of Rn Manifolds where ergodicity is not generic Noncompact manifolds and ends Ergodic homeomorphisms: the results Ergodic homeomorphisms: proofs Other properties typical in M[X, u] |
| ctrlnum | (ZDB-20-CBO)CR9780511543180 (OCoLC)704481351 (DE-599)BVBBV043942125 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543180 |
| format | Electronic eBook |
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| id | DE-604.BV043942125 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511543180 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351095 |
| oclc_num | 704481351 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xix, 216 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) |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge University Press |
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| series2 | Cambridge tracts in mathematics |
| spelling | Alpern, Steve 1948- Verfasser (DE-588)143654365 aut Typical dynamics of volume preserving homeomorphisms Steve Alpern, V.S. Prasad Cambridge Cambridge University Press 2000 1 Online-Ressource (xix, 216 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 139 Volume preserving homeomorphisms of the cube Introduction to part I and II (compact manifolds) Measure preserving homeomorphisms Discrete approximations Transitive homeomorphisms of In and Rn Fixed points and area preservation Measure preserving lusin theorem Ergodic homeomorphisms Uniform approximation in g[In, delta] and generic properties in M[In, delta] Measure preserving homeomorphisms of a compact manifold Measures on compact manifolds Dynamics on compact manifolds Oeasure preserving homeomorphisms of a noncompact manifold Ergodic volume preserving homeomorphisms of Rn Manifolds where ergodicity is not generic Noncompact manifolds and ends Ergodic homeomorphisms: the results Ergodic homeomorphisms: proofs Other properties typical in M[X, u] This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley–Zehnder– Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property Homeomorphisms Measure-preserving transformations Maßraum (DE-588)4169057-6 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Homöomorphismus (DE-588)4352383-3 gnd rswk-swf Kompakte Mannigfaltigkeit (DE-588)4164848-1 gnd rswk-swf Homöomorphismus (DE-588)4352383-3 s Kompakte Mannigfaltigkeit (DE-588)4164848-1 s Maßraum (DE-588)4169057-6 s Dynamik (DE-588)4013384-9 s DE-604 Skanda Prasad, V. S. 1949- Sonstige (DE-588)172376777 oth Erscheint auch als Druck-Ausgabe 978-0-521-58287-2 Erscheint auch als Druck-Ausgabe 978-0-521-17243-1 https://doi.org/10.1017/CBO9780511543180 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Alpern, Steve 1948- Typical dynamics of volume preserving homeomorphisms Volume preserving homeomorphisms of the cube Introduction to part I and II (compact manifolds) Measure preserving homeomorphisms Discrete approximations Transitive homeomorphisms of In and Rn Fixed points and area preservation Measure preserving lusin theorem Ergodic homeomorphisms Uniform approximation in g[In, delta] and generic properties in M[In, delta] Measure preserving homeomorphisms of a compact manifold Measures on compact manifolds Dynamics on compact manifolds Oeasure preserving homeomorphisms of a noncompact manifold Ergodic volume preserving homeomorphisms of Rn Manifolds where ergodicity is not generic Noncompact manifolds and ends Ergodic homeomorphisms: the results Ergodic homeomorphisms: proofs Other properties typical in M[X, u] Homeomorphisms Measure-preserving transformations Maßraum (DE-588)4169057-6 gnd Dynamik (DE-588)4013384-9 gnd Homöomorphismus (DE-588)4352383-3 gnd Kompakte Mannigfaltigkeit (DE-588)4164848-1 gnd |
| subject_GND | (DE-588)4169057-6 (DE-588)4013384-9 (DE-588)4352383-3 (DE-588)4164848-1 |
| title | Typical dynamics of volume preserving homeomorphisms |
| title_alt | Volume preserving homeomorphisms of the cube Introduction to part I and II (compact manifolds) Measure preserving homeomorphisms Discrete approximations Transitive homeomorphisms of In and Rn Fixed points and area preservation Measure preserving lusin theorem Ergodic homeomorphisms Uniform approximation in g[In, delta] and generic properties in M[In, delta] Measure preserving homeomorphisms of a compact manifold Measures on compact manifolds Dynamics on compact manifolds Oeasure preserving homeomorphisms of a noncompact manifold Ergodic volume preserving homeomorphisms of Rn Manifolds where ergodicity is not generic Noncompact manifolds and ends Ergodic homeomorphisms: the results Ergodic homeomorphisms: proofs Other properties typical in M[X, u] |
| title_auth | Typical dynamics of volume preserving homeomorphisms |
| title_exact_search | Typical dynamics of volume preserving homeomorphisms |
| title_full | Typical dynamics of volume preserving homeomorphisms Steve Alpern, V.S. Prasad |
| title_fullStr | Typical dynamics of volume preserving homeomorphisms Steve Alpern, V.S. Prasad |
| title_full_unstemmed | Typical dynamics of volume preserving homeomorphisms Steve Alpern, V.S. Prasad |
| title_short | Typical dynamics of volume preserving homeomorphisms |
| title_sort | typical dynamics of volume preserving homeomorphisms |
| topic | Homeomorphisms Measure-preserving transformations Maßraum (DE-588)4169057-6 gnd Dynamik (DE-588)4013384-9 gnd Homöomorphismus (DE-588)4352383-3 gnd Kompakte Mannigfaltigkeit (DE-588)4164848-1 gnd |
| topic_facet | Homeomorphisms Measure-preserving transformations Maßraum Dynamik Homöomorphismus Kompakte Mannigfaltigkeit |
| url | https://doi.org/10.1017/CBO9780511543180 |
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