Non-autonomous morse-decomposition and Lyapunov functions for gradient-like processes
We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) and prove that a non-autonomous gradient-like evolution process possesses a Morsedecomposition on the associated pullback attractor. We also prove the existence of an associated...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/22771 |
| Online Access: | http://hdl.handle.net/11441/22771 https://doi.org/10.1090/S0002-9947-2013-05810-2 |
| Access Level: | Open access |
| Keyword: | Non-autonomous Morse decomposition Lyapunov functions for nonautonomous dynamical systems robustness of dynamical structures |
| Summary: | We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) and prove that a non-autonomous gradient-like evolution process possesses a Morsedecomposition on the associated pullback attractor. We also prove the existence of an associated Lyapunov function which describes the gradient behavior of the system. Finally, we apply these abstract results to non-autonomous perturbations of autonomous gradient-like evolution processes (semigroups or autonomous dynamical systems). |
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