Three-Dimensional Flows

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.

First comprehensive treatment of this subject in book form Ease of reference to the main results in the theory with complete proofs and precise statements Complete proofs of several results which are spread throughout many different papers with a unified notation and approach Includes supplementary material: sn.pub/extras

Autorentext

Both authors are active researchers in the field of Dynamical Systems and Ergodic Theory. One is very young and the other well established in the field, being a coauthor of the main results in the theory.

Inhalt
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.