Speaker
Description
Classical contractive iterated function (IFSs) systems enjoy a remarkably rigid picture: a unique attractor, full symbolic coding, and robust asymptotic behavior. This picture changes substantially when the maps are defined only on prescribed local domains. In this talk, we present a framework for contractive local iterated function systems and investigate the structure and stability of their attractors. In contrast with the classical setting, the local attractor may contain endpoints corresponding to finite admissible orbits, its symbolic dynamics need not be of finite type, and different dynamical regimes may coexist within the same attractor, leading to a new notion of combinatorial instability. Joint work with E. Oliveira, UFRGS-Brazil.