Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability

Abstract

The present research project deals with the development of the theory of infinite-dimensional dynamical systems, associated with nonlinear evolution equations, and in particular with the study of the robustness of attractors for autonomous and non-autonomous dynamical systems under perturbations. This research topic is well recognized as an important research theme, even in the restricted context of autonomous dynamic systems (semigroups), and with applications to the development of applied areas such as Engineering and Natural Sciences. From the mathematical point of view, the theme is current and is studied in several well acquainted international research centers. Two centers stand out in the evolution of studies about the robustness of attractors for non-autonomous dynamic systems in the world, the ICMC-USP Non-Linear Dynamic Systems Group (SDNL) and the Stochastic Systems Differential Analysis Group (AESDIF) of the Faculty of Mathematics from the University of Seville.During the visit to the Universidad de Sevilla, the applicant (leader of the SDNL) intends to continue the development of the infinite-dimension dynamical systems theory in collaboration with Professors Tomás Caraballo Garrido (Full Professor - leader of AESDIF) and with outstanding researchers from the group such as Professor José Antonio Langa Rosado (Full Professor at AESDIF).