@ARTICLE{TBA, 

TITLE={[FORTHCOMING] Zip Shift encoding of M-TO-1 local homeomorphisms}, 
  
AUTHOR={Pouya Mehdipour
, Sanaz Lamei, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={}, 

NUMBER={Forthcoming papers<br>}, 
	
YEAR={2025}, 

URL={https://www.openscience.fr/Zip-Shift-encoding-of-M-TO-1-local-homeomorphisms}, 
	
DOI={TBA}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={We develop topological partitions for m-to-1 local homeomorphisms on compact metric spaces—maps that arise naturally in non-invertible dynamical systems, such as expanding and covering maps. These partitions enable a symbolic representation of the dynamics via the zip shift, an extended bilateral shift in the non-invertible setting. Inspired by Smale’s horseshoe construction, this approach generalizes topological partitions to a broader class of systems and opens new directions for studying their topological and ergodic properties.}}