For a dynamical system on a connected metric space X, the global attractor (when it exists) is connected provided that either the semigroup is time-continuous or X is locally connected. Moreover, there exists an example of a dynamical system on a connected metric space which admits a disconnected gl
Criteria on the Nonexistence of Invariant Lipschitz Submanifolds for Dynamical Systems
✍ Scribed by Michal Fečkan
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 227 KB
- Volume
- 174
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
✦ Synopsis
Conditions are given for smooth finite dimensional mappings which are precluding the existence of invariant Lipschitz compact submanifolds for those mappings. Flows, their discretizations, and their averagings are studied as well. Mappings and flows with constraints are also investigated.
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