NON-AUTONOMOUS MORSE-DECOMPOSITION AND LYAPUNOV FUNCTIONS FOR GRADIENT-LIKE PROCESSES

作者：Aragao Costa E R^*; Caraballo T; Carvalho A N; Langa J A

来源：Transactions of the American Mathematical Society, 2013, 365(10): 5277-5312.

• Non-autonomous Morse decomposition
• Lyapunov functions for non-autonomous dynamical systems
• robustness of dynamical structures

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 Morse-decomposition 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).

• 出版日期2013-10