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January  2007, 17(1): 107-119. doi: 10.3934/dcds.2007.17.107

Two-point pre-image entropy

Wen-Chiao Cheng 1,

1. 

Department of Mathematics, National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan, 621, Taiwan

Received  May 2005 Revised  April 2006 Published  October 2006

The aim of this paper is to define and study a new kind of entropy-like invariants in the case of probability space and compact metric topological group of continuous endomorphisms. These new invariants are only non-zero for non-invertible maps, but many propositions can be described and the analogue of the well-known variational principle can be established.
Keywords: Preimage entropy, Conditional entropy, Variational Principle..
Mathematics Subject Classification: Primary: 37A35; Secondary: 37B4.
Citation: Wen-Chiao Cheng. Two-point pre-image entropy. Discrete & Continuous Dynamical Systems, 2007, 17 (1) : 107-119. doi: 10.3934/dcds.2007.17.107
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