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OverviewSince at least the time of Poisson, mathematicians have pondered the notion of recurrence for differential equations. Solutions that exhibit recurrent behavior provide insight into the behavior of general solutions. In Recurrence and Topology, Alongi and Nelson provide a modern understanding of the subject, using the language and tools of dynamical systems and topology. Recurrence and Topology develops increasingly more general topological modes of recurrence for dynamical systems beginning with fixed points and concluding with chain recurrent points. For each type of recurrence the text provides detailed examples arising from explicit systems of differential equations; it establishes the general topological properties of the set of recurrent points; and it investigates the possibility of partitioning the set of recurrent points into subsets which are dynamically irreducible. The text includes a discussion of real-valued functions that reflect the structure of the sets of recurrent points and concludes with a thorough treatment of the Fundamental Theorem of Dynamical Systems.Recurrence and Topology is appropriate for mathematics graduate students, though a well-prepared undergraduate might read most of the text with great benefit. Full Product DetailsAuthor: John M. Alongi , Gail S. NelsonPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated edition Volume: No. 85 Weight: 0.580kg ISBN: 9780821842348ISBN 10: 082184234 Pages: 221 Publication Date: 30 July 2007 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsFlows Recurrent points Irreducible sets Test functions Afterword Appendix A. Discrete dynamical systems Appendix B. Circle rotations Appendix C. The Hausdorff metric Bibliography Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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