Geodesic
Pre-image entropy for maps on noncompact topological spaces
Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 2, pp. 219-230 
Lei Liu; Lei Liu. Pre-image entropy for maps on noncompact topological spaces. Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 2, pp. 219-230. http://geodesic.mathdoc.fr/item/AMUC_2013_82_2_a6/
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     author = {Lei Liu and Lei Liu},
     title = { Pre-image entropy for maps on noncompact topological spaces},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {219--230},
     year = {2013},
     volume = {82},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2013_82_2_a6/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.