Recurrence and topology
著者
書誌事項
Recurrence and topology
（Graduate studies in mathematics, v. 85）
American Mathematical Society, c2007
大学図書館所蔵 件 / 全36件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 213-215) and index
内容説明・目次
内容説明
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.
目次
Flows Recurrent points Irreducible sets Test functions Afterword Appendix A. Discrete dynamical systems Appendix B. Circle rotations Appendix C. The Hausdorff metric Bibliography Index.
「Nielsen BookData」 より