Recurrence and Topology

Recurrence and Topology

Pub. Date:
American Mathematical Society

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Recurrence and Topology

Since 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.

Product Details

ISBN-13: 9780821842348
Publisher: American Mathematical Society
Publication date: 07/25/2007
Series: Graduate Studies in Mathematics Series , #85
Pages: 221
Sales rank: 1,075,799
Product dimensions: 10.10(w) x 7.20(h) x 0.80(d)

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