This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse...
This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensi...
The Theory of Dynamical Systems was first introduced by the great mathematician Henri Poincare as a qualitative study of differential equations. For more than forty years, Jacob Palis has made outstanding contributions to this area of mathematics. In the 1970s, following in the wake of Stephen Smale, he became one of the major figures in developing the Theory of Hyperbolic Dynamics and Structural Stability.
This volume presents a selection of Jacob Palis' mathematical contributions, starting with his PhD thesis and ending with papers on what is widely known as the Palis Conjecture....
The Theory of Dynamical Systems was first introduced by the great mathematician Henri Poincare as a qualitative study of differential equations. Fo...
