| Description |
1 online resource (xix, 358 pages) : illustrations |
| Series |
Ergebnisse der Mathematik und ihrer Grenzgebiete = A series of modern surveys in mathematics ; 3 folge, v. 53 |
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Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 53
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| Contents |
880-01 Preliminary Definitions and Results -- Singular Cycles and Robust Singular Attractors -- Robustness on the Whole Ambient Space -- Robust Transitivity and Singular-Hyperbolicity -- Singular-Hyperbolicity and Robustness -- Expansiveness and Physical Measure -- Singular-Hyperbolicity and Volume -- Global Dynamics of Generic 3-Flows -- Related Results and Recent Developments |
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880-01/(S Contents note continued: 6.3.1. Denseness of Periodic Orbits and Transitivity with a Unique Singularity -- 6.3.2. Unstable Manifolds of Periodic Orbits Inside Singular-Hyperbolic Attractors -- 7. Expansiveness and Physical Measure -- 7.1. Statements of the Results and Overview of the Arguments -- 7.1.1. Robust Sensitiveness -- 7.1.2. Existence and Uniqueness of a Physical Measure -- 7.2. Expansiveness -- 7.2.1. Proof of Expansiveness -- 7.2.2. Infinitely Many Coupled Returns -- 7.2.3. Semi-global Poincare Map -- 7.2.4.A Tube-Like Domain Without Singularities -- 7.2.5. Every Orbit Leaves the Tube -- 7.2.6. The Poincare Map Is Well-Defined on Σj -- 7.2.7. Expansiveness of the Poincare Map -- 7.2.8. Singular-Hyperbolicity and Chaotic Behavior -- 7.3. Non-uniform Hyperbolicity -- 7.3.1. The Starting Point -- 7.3.2. The Holder Property of the Projection -- 7.3.3. Integrability of the Global Return Time -- 7.3.4. Suspending Invariant Measures -- 7.3.5. Physical Measure for the Global Poincare Map |
| Summary |
In this book, the authors present the elements of a general theory for flows on three-dimensional compact boundaryless manifolds, encompassing flows with equilibria accumulated by regular orbits. The book aims to provide a global perspective of this theory and make it easier for the reader to digest the growing literature on this subject. This is not the first book on the subject of dynamical systems, but there are distinct aspects which together make this book unique. Firstly, this book treats mostly continuous time dynamical systems, instead of its discrete counterpart, exhaustively treated in some other texts. Secondly, this book treats all the subjects from a mathematical perspective with proofs of most of the results included. Thirdly, this book is meant to be an advanced graduate textbook and not just a reference book or monograph on the subject. This aspect is reflected in the way the cover material is presented, with careful and complete proofs, and precise references to topics in the book |
| Bibliography |
Includes bibliographical references (pages 343-353) and index |
| Notes |
Print version record |
| Subject |
Flows (Differentiable dynamical systems)
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MATHEMATICS -- Geometry -- General.
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Ecuaciones diferenciales
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Flows (Differentiable dynamical systems)
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Dynamisches System
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Hyperbolizität
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Fluss Mathematik
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Kompakte Mannigfaltigkeit
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Hyperbolizitèat.
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| Form |
Electronic book
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| Author |
Pacifico, Maria José
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| ISBN |
9783642114144 |
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3642114148 |
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