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Random dynamical systems
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.
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Cited by
The synchronization of chaotic systems
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00137-0 · Cited by 2,764
Attractors for random dynamical systems
Crauel, H., & Flandoli, F. (1994) · Probability Theory and Related Fields · doi:10.1007/bf01193705 · Cited by 985
Answering Schrödinger's question: A free-energy formulation
Ramstead, M. J. D., Badcock, P. B., & Friston, K. J. (2018) · Physics of Life Reviews · doi:10.1016/j.plrev.2017.09.001 · Cited by 354
On markov blankets and hierarchical self-organisation
Palacios, E. R., Razi, A., Parr, T., Kirchhoff, M., & Friston, K. (2020) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2019.110089 · Cited by 115
Global random attractors are uniquely determined by attracting deterministic compact sets
Crauel, H. (1999) · Annali di Matematica Pura ed Applicata · doi:10.1007/bf02505989 · Cited by 108
Metadata
- Venue
- Interdisciplinary Mathematical Sciences
- Publisher
- WORLD SCIENTIFIC
- Published
- 2020-12
- Pages
- 117-126
- ISSN
- 1793-1355 (ISSN-L)
- OpenAlex
- W1802196594
- Cited by
- 2,127
- References
- 0
- FWCI
- 500.03
- Type
- book chapter
- Language
- en
- Open access
- closed
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