First, we talk about the topology of orbits of points under hyperbolic diffeomorphisms and the important theorem: Smale spectral decomposition. After that, we will talk about the structure of pre-images, pre-orbits, and limit sets, under Anosov endomorphisms, and some important topological properties of those sets under endomorphisms. Especially linear Anosov endomorphisms over tori. In this regard, we consider a fixed point and its pre-images under a linear endomorphism over as a lattice in. This talk is based on the works of Feliks Przytycki; My Ph.D. thesis, and the book ...


[IPM Youth Seminars on Topology and Dynamics]