Three-Dimensional Flows (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Book 53)

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. Front Matter....Pages I-XIX Introduction....Pages 1-4 Preliminary Definitions and Results....Pages 5-54 Singular Cycles and Robust Singular Attractors....Pages 55-97 Robustness on the Whole Ambient Space....Pages 99-121 Robust Transitivity and Singular-Hyperbolicity....Pages 123-161 Singular-Hyperbolicity and Robustness....Pages 163-202 Expansiveness and Physical Measure....Pages 203-248 Singular-Hyperbolicity and Volume....Pages 249-268 Global Dynamics of Generic 3-Flows....Pages 269-308 Related Results and Recent Developments....Pages 309-323 Back Matter....Pages 325-358 Xxx 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. Vítor Araújo, Maria José Pacifico. Includes Bibliographical References (p. 343-353) And Index.