Three-Dimensional Flows [electronic resource] /
Araújo, Vítor.author.
Pacifico, Maria José.author.
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.
Description based upon print version of record.
Includes bibliographical references (p. 343-353) and index.
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.
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.
Dynamics.
Ergodic theory.
Differential equations.
Mathematical physics.
Dynamical Systems and Ergodic Theory.
Ordinary Differential Equations.
Theoretical, Mathematical and Computational Physics.