Random dynamical systems

著者

• Arnold, L. (Ludwig)

書誌事項

Random dynamical systems

Ludwig Arnold

（Springer monographs in mathematics）

Springer, c2010

• : pbk

注記

Includes bibliographical references (p. [563]-580) and index

内容説明・目次

内容説明

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

目次

I. Random Dynamical Systems and Their Generators.- 1. Basic Definitions. Invariant Measures.- 2. Generation.- II. Multiplicative Ergodic Theory.- 3. The Multiplicative Ergodic Theorem in Euclidean Space.- 4. The Multiplicative Ergodic Theorem on Bundles and Manifolds.- 5. The MET for Related Linear and Affine RDS.- 6. RDS on Homogeneous Spaces of the General Linear Group.- III. Smooth Random Dynamical Systems.- 7. Invariant Manifolds.- 8. Normal Forms.- 9. Bifurcation Theory.- IV. Appendices.- Appendix A. Measurable Dynamical Systems.- A.1 Ergodic Theory.- A.2 Stochastic Processes and Dynamical Systems.- A.3 Stationary Processes.- A.4 Markov Processes.- Appendix B. Smooth Dynamical Systems.- B.1 Two-Parameter Flows on a Manifold.- B.4 Autonomous Case: Dynamical Systems.- B.5 Vector Fields and Flows on Manifolds.- References.

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詳細情報

• NII書誌ID(NCID): BB09631078
• ISBN:
  • 9783642083556
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: xv, 586 p.
• 大きさ: 25 cm
• 分類:
  • LCC : QA274.23
  • DC21 : 519.2
  • NDC8 : 417.1
• 件名:
  • LCSH : Stochastic differential equations
  • LCSH : Differentiable dynamical systems
  • LCSH : Ergodic theory
• 親書誌ID:
  • BA3386797X