Random Dynamical Systems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-662-12878-7 |
| Beschreibung: | This book is the first systematic presentation of the theory of random dynamical systems, i.e. of dynamical systems under the influence of some kind of randomness. The theory comprises products of random mappings as well as random and stochastic differential equations. The author's approach is based on Oseledets'multiplicative ergodic theorem for linear random systems, for which a detailed proof is presented. This theorem provides us with a random substitute of linear algebra and hence can serve as the basis of a local theory of nonlinear random systems. In particular, global and local random invariant manifolds are constructed and their regularity is proved. Techniques for simplifying a system by random continuous or smooth coordinate tranformations are developed (random Hartman-Grobman theorem, random normal forms). Qualitative changes in families of random systems (random bifurcation theory) are also studied. A dynamical approach is proposed which is based on sign changes of Lyapunov exponents and which extends the traditional phenomenological approach based on the Fokker-Planck equation. Numerous instructive examples are treated analytically or numerically. The main intention is, however, to present a reliable and rather complete source of reference which lays the foundations for future works and applications |
| Umfang: | 1 Online-Ressource (XV, 586 p) |
| ISBN: | 9783662128787 9783642083556 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-12878-7 |
Internformat
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| 500 | |a This book is the first systematic presentation of the theory of random dynamical systems, i.e. of dynamical systems under the influence of some kind of randomness. The theory comprises products of random mappings as well as random and stochastic differential equations. The author's approach is based on Oseledets'multiplicative ergodic theorem for linear random systems, for which a detailed proof is presented. This theorem provides us with a random substitute of linear algebra and hence can serve as the basis of a local theory of nonlinear random systems. In particular, global and local random invariant manifolds are constructed and their regularity is proved. Techniques for simplifying a system by random continuous or smooth coordinate tranformations are developed (random Hartman-Grobman theorem, random normal forms). Qualitative changes in families of random systems (random bifurcation theory) are also studied. A dynamical approach is proposed which is based on sign changes of Lyapunov exponents and which extends the traditional phenomenological approach based on the Fokker-Planck equation. Numerous instructive examples are treated analytically or numerically. The main intention is, however, to present a reliable and rather complete source of reference which lays the foundations for future works and applications | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Arnold, Ludwig |
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| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-12878-7 |
| format | Electronic eBook |
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| id | DE-604.BV042423484 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:48Z |
| institution | BVB |
| isbn | 9783662128787 9783642083556 |
| issn | 1439-7382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858901 |
| oclc_num | 905373681 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XV, 586 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Springer Monographs in Mathematics |
| spellingShingle | Arnold, Ludwig Random Dynamical Systems Mathematics Differentiable dynamical systems Systems theory Distribution (Probability theory) Engineering mathematics Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Systems Theory, Control Appl.Mathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics Mathematik Zufälliges dynamisches System (DE-588)4335207-8 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Ergodische Kette (DE-588)4402921-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4335207-8 (DE-588)4057621-8 (DE-588)4402921-4 (DE-588)4137931-7 (DE-588)4013396-5 |
| title | Random Dynamical Systems |
| title_auth | Random Dynamical Systems |
| title_exact_search | Random Dynamical Systems |
| title_full | Random Dynamical Systems by Ludwig Arnold |
| title_fullStr | Random Dynamical Systems by Ludwig Arnold |
| title_full_unstemmed | Random Dynamical Systems by Ludwig Arnold |
| title_short | Random Dynamical Systems |
| title_sort | random dynamical systems |
| topic | Mathematics Differentiable dynamical systems Systems theory Distribution (Probability theory) Engineering mathematics Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Systems Theory, Control Appl.Mathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics Mathematik Zufälliges dynamisches System (DE-588)4335207-8 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Ergodische Kette (DE-588)4402921-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Mathematics Differentiable dynamical systems Systems theory Distribution (Probability theory) Engineering mathematics Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Statistical Physics, Dynamical Systems and Complexity Systems Theory, Control Appl.Mathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics Mathematik Zufälliges dynamisches System Stochastische Differentialgleichung Ergodische Kette Differenzierbares dynamisches System Dynamisches System |
| url | https://doi.org/10.1007/978-3-662-12878-7 |
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