On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
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| Schriftenreihe: | Springer Monographs in Mathematics
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing |
| Beschreibung: | 1 Online-Ressource (VII, 144 p) |
| ISBN: | 9783662090701 9783642072642 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-09070-1 |
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662090701 9783642072642 |
| issn | 1439-7382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858835 |
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| publishDate | 2004 |
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| spelling | Margulis, Grigoriy A. Verfasser aut On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (VII, 144 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik https://doi.org/10.1007/978-3-662-09070-1 Verlag Volltext |
| spellingShingle | Margulis, Grigoriy A. On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik |
| title | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| title_auth | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| title_exact_search | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| title_full | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis |
| title_fullStr | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis |
| title_full_unstemmed | On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows by Grigoriy A. Margulis |
| title_short | On Some Aspects of the Theory of Anosov Systems |
| title_sort | on some aspects of the theory of anosov systems with a survey by richard sharp periodic orbits of hyperbolic flows |
| title_sub | With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
| topic | Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik |
| topic_facet | Mathematics Differentiable dynamical systems Geometry Dynamical Systems and Ergodic Theory Mathematik |
| url | https://doi.org/10.1007/978-3-662-09070-1 |
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