Academic Journals Database
Disseminating quality controlled scientific knowledge

Pre-image entropy for maps on noncompact topological spaces

Author(s): Lei Liu

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXII;
Issue: 2;
Start page: 219;
Date: 2013;
VIEW PDF   PDF DOWNLOAD PDF   Download PDF Original page

Keywords: Pre-image entropy | Locally compact space | Alexandroff compactification | hyperspace dynamical system

We propose a new definition of pre-imageentropy for continuous maps on noncompact topological spaces,investigate fundamental properties of the new pre-image entropy, andcompare the new pre-image entropy with the existing ones. Thedefined 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.
RPA Switzerland

RPA Switzerland

Robotic process automation


Tango Rapperswil
Tango Rapperswil