arXiv subjects
Publications and source records attributed to Margoth Tacuri.
We introduce distinct definitions of local stable/unstable sets for flows without fixed points, namely, kinematic, geometric, and sectionally geometric, and discuss relations between them. We prove the existence of continua with a uniform diameter within each sectionally geometric local stable/unstable set for cw-expansive flows defined on Peano continua.
In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary we generalize results in [6] and [11] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countably spaces.