A first course in dynamics: with a panorama of recent developments
The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
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| Links: | https://doi.org/10.1017/CBO9780511998188 |
| Zusammenfassung: | The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory. |
| Umfang: | 1 Online-Ressource (x, 424 Seiten) |
| ISBN: | 9780511998188 |
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| spelling | Hasselblatt, Boris A first course in dynamics with a panorama of recent developments Boris Hasselblatt, Anatole Katok Cambridge Cambridge University Press 2003 1 Online-Ressource (x, 424 Seiten) txt c cr The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory. Katok, A. B. Erscheint auch als Druck-Ausgabe 9780521583046 Erscheint auch als Druck-Ausgabe 9780521587501 |
| spellingShingle | Hasselblatt, Boris A first course in dynamics with a panorama of recent developments |
| title | A first course in dynamics with a panorama of recent developments |
| title_auth | A first course in dynamics with a panorama of recent developments |
| title_exact_search | A first course in dynamics with a panorama of recent developments |
| title_full | A first course in dynamics with a panorama of recent developments Boris Hasselblatt, Anatole Katok |
| title_fullStr | A first course in dynamics with a panorama of recent developments Boris Hasselblatt, Anatole Katok |
| title_full_unstemmed | A first course in dynamics with a panorama of recent developments Boris Hasselblatt, Anatole Katok |
| title_short | A first course in dynamics |
| title_sort | first course in dynamics with a panorama of recent developments |
| title_sub | with a panorama of recent developments |
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