Dynamical system and chaos: an introduction with applications
This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical syste...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2023]
|
| Schriftenreihe: | UNITEXT for physics
|
| Schlagworte: | |
| Zusammenfassung: | This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful.The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters |
| Beschreibung: | Differential Equations as Dynamical Systems.- Stability of fixed points.- Difference equations as dynamical systems.- Classification of fixed points.- Hamiltonian systems.- Numerical Methods.-Strange Attractors and Maps of an Interval.- Stable, Unstable and Centre manifolds.-Dynamics in the Centre Manifold.- Lyapunov Exponents and Oseledets Theorem.- Chaos.- Limit and Recurrent Sets.-Poincare Maps.- The Poincare-Bendixon Theorem.- Bifurcations of Differential Equations.-Singular Pertubations and Ducks.-Strange Attractors in Delay Equations.- Complexity of Strange Attractors.-Intermittency.- Cellular Automata.- Maps of the Complex Plane.- Stochastic Iteration of Function Systems.- Linear Maps on the Torus and Symbolic Dynamics.- Parametric Resonance.- Robot Motion.- Synchronisation of Pendula.- Synchronisation of Clocks.- Chaos in Stormer Problem.-Introduction to Celestial mechanics.- Introduction to non-Liner control Theory.- Appendices |
| Beschreibung: | ix, 326 Seiten Illustrationen, Diagramme 731 grams |
| ISBN: | 9783031251535 9783031251566 |
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| 520 | |a This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful.The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters | ||
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| 653 | |a Hardcover, Softcover / Physik, Astronomie/Theoretische Physik | ||
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-25154-2 |
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Datensatz im Suchindex
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| bvnumber | BV049064039 |
| classification_rvk | UG 3900 |
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| discipline | Physik |
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| id | DE-604.BV049064039 |
| illustrated | Illustrated |
| index_date | 2024-07-03T22:25:03Z |
| indexdate | 2024-07-20T08:36:34Z |
| institution | BVB |
| isbn | 9783031251535 9783031251566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034326129 |
| oclc_num | 1401213077 |
| open_access_boolean | |
| owner | DE-29T DE-703 |
| owner_facet | DE-29T DE-703 |
| physical | ix, 326 Seiten Illustrationen, Diagramme 731 grams |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Springer |
| record_format | marc |
| series2 | UNITEXT for physics |
| spelling | Dilão, Rui Verfasser aut Dynamical system and chaos an introduction with applications Rui Dilão Cham, Switzerland Springer [2023] ix, 326 Seiten Illustrationen, Diagramme 731 grams txt rdacontent n rdamedia nc rdacarrier UNITEXT for physics Differential Equations as Dynamical Systems.- Stability of fixed points.- Difference equations as dynamical systems.- Classification of fixed points.- Hamiltonian systems.- Numerical Methods.-Strange Attractors and Maps of an Interval.- Stable, Unstable and Centre manifolds.-Dynamics in the Centre Manifold.- Lyapunov Exponents and Oseledets Theorem.- Chaos.- Limit and Recurrent Sets.-Poincare Maps.- The Poincare-Bendixon Theorem.- Bifurcations of Differential Equations.-Singular Pertubations and Ducks.-Strange Attractors in Delay Equations.- Complexity of Strange Attractors.-Intermittency.- Cellular Automata.- Maps of the Complex Plane.- Stochastic Iteration of Function Systems.- Linear Maps on the Torus and Symbolic Dynamics.- Parametric Resonance.- Robot Motion.- Synchronisation of Pendula.- Synchronisation of Clocks.- Chaos in Stormer Problem.-Introduction to Celestial mechanics.- Introduction to non-Liner control Theory.- Appendices This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful.The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters Dynamical systems Mathematical physics System theory Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Hardcover, Softcover / Physik, Astronomie/Theoretische Physik Dynamisches System (DE-588)4013396-5 s Chaotisches System (DE-588)4316104-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-031-25154-2 |
| spellingShingle | Dilão, Rui Dynamical system and chaos an introduction with applications Dynamical systems Mathematical physics System theory Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4316104-2 |
| title | Dynamical system and chaos an introduction with applications |
| title_auth | Dynamical system and chaos an introduction with applications |
| title_exact_search | Dynamical system and chaos an introduction with applications |
| title_exact_search_txtP | Dynamical system and chaos an introduction with applications |
| title_full | Dynamical system and chaos an introduction with applications Rui Dilão |
| title_fullStr | Dynamical system and chaos an introduction with applications Rui Dilão |
| title_full_unstemmed | Dynamical system and chaos an introduction with applications Rui Dilão |
| title_short | Dynamical system and chaos |
| title_sort | dynamical system and chaos an introduction with applications |
| title_sub | an introduction with applications |
| topic | Dynamical systems Mathematical physics System theory Dynamisches System (DE-588)4013396-5 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Dynamical systems Mathematical physics System theory Dynamisches System Chaotisches System |
| work_keys_str_mv | AT dilaorui dynamicalsystemandchaosanintroductionwithapplications |