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arXiv · 2502.11272

Zip shift Space

Sanaz Lamei·Pouya Mehdipour
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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.

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Sanaz Lamei, Pouya Mehdipour. 2025-02-16. Zip shift Space. https://arxiv.org/abs/2502.11272

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