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 explained 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.
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-0497-1 (9780821804971)
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Schweitzer Klassifikation
Introduction Preliminaries Bifurcations in the plane Homoclinic orbits of nonhyperbolic singular points Homoclinic tori and Klein bottles of nonhyperbolic periodic orbits: Noncritical case Homoclinic torus of a nonhyperbolic periodic orbit: Semicritical case Bifurcations of homoclinic trajectories of hyperbolic saddles Elements of hyperbolic theory Normal forms for local families: Hyperbolic case Normal forms for unfoldings of saddlenodes Bibliography.
