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OverviewThis 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. Full Product DetailsAuthor: Yu Il'yashenko , Li WeiguPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: v. 66 Weight: 0.737kg ISBN: 9780821804971ISBN 10: 0821804979 Pages: 286 Publication Date: 30 October 1998 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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