Recurrence and Topology
2007
American Mathematical Society (Verlag)
978-0-8218-4234-8 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4234-8 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei innerhalb Deutschlands
- Auch auf Rechnung
- Verfügbarkeit in der Filiale vor Ort prüfen
- Artikel merken
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. This text provides a modern understanding of the subject, using the language and tools of dynamical systems 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.
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.
Flows Recurrent points Irreducible sets Test functions Afterword Appendix A. Discrete dynamical systems Appendix B. Circle rotations Appendix C. The Hausdorff metric Bibliography Index.
Erscheint lt. Verlag | 30.7.2007 |
---|---|
Reihe/Serie | Graduate Studies in Mathematics |
Zusatzinfo | Illustrations |
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 580 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-8218-4234-X / 082184234X |
ISBN-13 | 978-0-8218-4234-8 / 9780821842348 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Grundlagen, Beispiele, Aufgaben, Lösungen
Buch | Hardcover (2022)
Hanser, Carl (Verlag)
29,99 €