Zip shift Space
Dynamical Systems
2025-02-18 v1 Mathematical Physics
math.MP
Chaotic Dynamics
Abstract
We introduce a new extension in symbolic dynamics on two sets of alphabets, called the zip shift space. In finite case, it represents a finite-to-1 local homeomorphism called zip shift map. Such extension, offers a conjugacy between some endomorphisms and some zip shift map over two-sided space with finite sets of alphabets. As an application, the topological conjugacy of an N-to-1 uniformly hyperbolic horseshoe map with a zip shift map and its orbit structure is investigated. Moreover, the pre-image studies over zip shift space and the concepts of stable and unstable sets and homoclinic orbits, with a precise description for N-to-1 horseshoe are illustrated.
Cite
@article{arxiv.2502.11272,
title = {Zip shift Space},
author = {Sanaz Lamei and Pouya Mehdipour},
journal= {arXiv preprint arXiv:2502.11272},
year = {2025}
}