Nonlocal Bifurcations

Download or read book Nonlocal Bifurcations written by I︠U︡. S. Ilʹi︠a︡shenko and published by American Mathematical Soc.. This book was released on 1999 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. These bifurcations provide a series of fascinating new scenarios for the transition from simple dynamical systems to complicated ones. The main effects are the generation of hyperbolic periodic orbits, nontrivial hyperbolic invariant sets and the elements of hyperbolic theory. All results are rigorously proved and exposed in a uniform way. The foundations of normal forms and hyperbolic theories are presented from the very first stages. The proofs are preceded by heuristic descriptions of the ideas. The book contains new results, and many results have not previously appeared in monograph form.