Abstract
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.
Keywords
Statistical physicsComputer sciencePhysics
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Publication Info
- Year
- 2020
- Type
- book-chapter
- Pages
- 117-126
- Citations
- 2211
- Access
- Closed
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Cite This
Ludwig Arnold
(2020).
Random dynamical systems.
Interdisciplinary mathematical sciences
, 117-126.
https://doi.org/10.1142/9789811228667_0013
Identifiers
- DOI
- 10.1142/9789811228667_0013