Shadowing properties for infinite dimensional dynamical systems

Carlos Roberto Takaessu Junior - SUSTech, China

Abstract:

  In this talk, we show that certain Morse–Smale dynamical systems defined on Hilbert spaces exhibit the Lipschitz Shadowing property on their global attractors and the Hölder Shadowing property in a neighborhood of the attractors. This result extends classical theorems on shadowing for dynamical systems on compact manifolds to the infinite-dimensional setting. We also discuss several applications, including results on the continuity of attractors and the stability of infinite-dimensional Morse–Smale systems.