Geometric Theory of Dynamical Systems: An Introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1982
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | ... cette etude qualitative (des equations difj'erentielles) aura par elle-m~me un inter~t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations |
| Beschreibung: | 1 Online-Ressource (XII, 198 p) |
| ISBN: | 9781461257035 9781461257059 |
| DOI: | 10.1007/978-1-4612-5703-5 |
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| 500 | |a ... cette etude qualitative (des equations difj'erentielles) aura par elle-m~me un inter~t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations | ||
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Datensatz im Suchindex
| _version_ | 1804153092290117632 |
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| any_adam_object | |
| author | Palis, Jacob |
| author_facet | Palis, Jacob |
| author_role | aut |
| author_sort | Palis, Jacob |
| author_variant | j p jp |
| building | Verbundindex |
| bvnumber | BV042420418 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863938012 (DE-599)BVBBV042420418 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-5703-5 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461257035 9781461257059 |
| language | English |
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| spelling | Palis, Jacob Verfasser aut Geometric Theory of Dynamical Systems An Introduction by Jacob Palis, Welington Melo New York, NY Springer US 1982 1 Online-Ressource (XII, 198 p) txt rdacontent c rdamedia cr rdacarrier ... cette etude qualitative (des equations difj'erentielles) aura par elle-m~me un inter~t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations Mathematics Mathematics, general Theoretical, Mathematical and Computational Physics Mathematik Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Globale Analysis (DE-588)4021285-3 s 1\p DE-604 Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 2\p DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s 3\p DE-604 Melo, Welington Sonstige oth https://doi.org/10.1007/978-1-4612-5703-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Palis, Jacob Geometric Theory of Dynamical Systems An Introduction Mathematics Mathematics, general Theoretical, Mathematical and Computational Physics Mathematik Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Globale Analysis (DE-588)4021285-3 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4012269-4 (DE-588)4137931-7 (DE-588)4021285-3 (DE-588)4013396-5 |
| title | Geometric Theory of Dynamical Systems An Introduction |
| title_auth | Geometric Theory of Dynamical Systems An Introduction |
| title_exact_search | Geometric Theory of Dynamical Systems An Introduction |
| title_full | Geometric Theory of Dynamical Systems An Introduction by Jacob Palis, Welington Melo |
| title_fullStr | Geometric Theory of Dynamical Systems An Introduction by Jacob Palis, Welington Melo |
| title_full_unstemmed | Geometric Theory of Dynamical Systems An Introduction by Jacob Palis, Welington Melo |
| title_short | Geometric Theory of Dynamical Systems |
| title_sort | geometric theory of dynamical systems an introduction |
| title_sub | An Introduction |
| topic | Mathematics Mathematics, general Theoretical, Mathematical and Computational Physics Mathematik Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Globale Analysis (DE-588)4021285-3 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Mathematics Mathematics, general Theoretical, Mathematical and Computational Physics Mathematik Differenzierbare Mannigfaltigkeit Differenzierbares dynamisches System Globale Analysis Dynamisches System |
| url | https://doi.org/10.1007/978-1-4612-5703-5 |
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