Square entropy, the geometric mean of forward and backward entropies, is claimed to be a complete isomorphism invariant for uniform n-to-1 full zip shift maps.
Zip shift Space
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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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Square Entropy and Uniform n-to-1 Bernoulli Transformations
Square entropy, the geometric mean of forward and backward entropies, is claimed to be a complete isomorphism invariant for uniform n-to-1 full zip shift maps.