Pre-image entropy for maps on noncompact topological spaces

Main Article Content

Lei Liu

Abstract

We propose a new definition of pre-image entropy for continuous maps on noncompact topological spaces, investigate fundamental properties of the new pre-image entropy, and compare the new pre-image entropy with the existing ones. The defined pre-image entropy generates that of Cheng and Newhouse. Yet, it holds various basic properties of Cheng and Newhouse's pre-image entropy, for example, the pre-image entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have the same pre-image entropy, the pre-image entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new pre-image entropy coincides with Cheng and Newhouse's pre-image entropy for compact systems.

Article Details

How to Cite
Liu, L. (2017). Pre-image entropy for maps on noncompact topological spaces. Acta Mathematica Universitatis Comenianae, 82(2), 219-230. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/742/497
Section
Articles