Interdisciplinary mathematical sciences· 2020Q2· Book chapter
Random dynamical systems
- 2,237citations
- Q2SCImago
- 2020year
Short summary
This work provides a comprehensive mathematical framework for understanding random dynamical systems (RDS) and their generators, detailing key theoretical concepts and advanced techniques.
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Key points
- Defines basic concepts and invariant measures for random dynamical systems.
- Presents the Multiplicative Ergodic Theorem for various mathematical spaces.
- Investigates smooth random dynamical systems, invariant manifolds, and bifurcation theory.
- Includes appendices on measurable and smooth dynamical systems for foundational context.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Interdisciplinary mathematical sciences, 2020 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics