American Institute of Mathematical Sciences

Advanced
  • Previous Article
    On a nonlinear Schrödinger equation modelling ultra-short laser pulses with a large noncompact global attractor
  • DCDS Home
  • This Issue
  • Next Article
    Characteristic equation approach to stability measures of linear neutral systems with multiple time delays
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
[1]

Yujun Zhu. Preimage entropy for random dynamical systems. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 829-851. doi: 10.3934/dcds.2007.18.829
[2]

Ping Huang, Ercai Chen, Chenwei Wang. Entropy formulae of conditional entropy in mean metrics. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 5129-5144. doi: 10.3934/dcds.2018226
[3]

Xiaomin Zhou. A formula of conditional entropy and some applications. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 4063-4075. doi: 10.3934/dcds.2016.36.4063
[4]

Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 6581-6597. doi: 10.3934/dcds.2016085
[5]

Zheng Yin, Ercai Chen. The conditional variational principle for maps with the pseudo-orbit tracing property. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 463-481. doi: 10.3934/dcds.2019019
[6]

Artur O. Lopes, Elismar R. Oliveira. Entropy and variational principles for holonomic probabilities of IFS. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 937-955. doi: 10.3934/dcds.2009.23.937
[7]

Jessy Mallet, Stéphane Brull, Bruno Dubroca. General moment system for plasma physics based on minimum entropy principle. Kinetic & Related Models, 2015, 8 (3) : 533-558. doi: 10.3934/krm.2015.8.533
[8]

Michael Brandenbursky, Michał Marcinkowski. Entropy and quasimorphisms. Journal of Modern Dynamics, 2019, 15: 143-163. doi: 10.3934/jmd.2019017
[9]

Wenxiang Sun, Cheng Zhang. Zero entropy versus infinite entropy. Discrete & Continuous Dynamical Systems, 2011, 30 (4) : 1237-1242. doi: 10.3934/dcds.2011.30.1237
[10]

Yixiao Qiao, Xiaoyao Zhou. Zero sequence entropy and entropy dimension. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 435-448. doi: 10.3934/dcds.2017018
[11]

Yunkyong Hyon, José A. Carrillo, Qiang Du, Chun Liu. A maximum entropy principle based closure method for macro-micro models of polymeric materials. Kinetic & Related Models, 2008, 1 (2) : 171-184. doi: 10.3934/krm.2008.1.171
[12]

Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2367-2381. doi: 10.3934/dcdsb.2014.19.2367
[13]

José M. Amigó, Karsten Keller, Valentina A. Unakafova. On entropy, entropy-like quantities, and applications. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3301-3343. doi: 10.3934/dcdsb.2015.20.3301
[14]

François Blanchard, Wen Huang. Entropy sets, weakly mixing sets and entropy capacity. Discrete & Continuous Dynamical Systems, 2008, 20 (2) : 275-311. doi: 10.3934/dcds.2008.20.275
[15]

Boris Kruglikov, Martin Rypdal. Entropy via multiplicity. Discrete & Continuous Dynamical Systems, 2006, 16 (2) : 395-410. doi: 10.3934/dcds.2006.16.395
[16]

Nicolas Bedaride. Entropy of polyhedral billiard. Discrete & Continuous Dynamical Systems, 2007, 19 (1) : 89-102. doi: 10.3934/dcds.2007.19.89
[17]

Karl Petersen, Ibrahim Salama. Entropy on regular trees. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 4453-4477. doi: 10.3934/dcds.2020186
[18]

Vladimír Špitalský. Local correlation entropy. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 5711-5733. doi: 10.3934/dcds.2018249
[19]

Baolin He. Entropy of diffeomorphisms of line. Discrete & Continuous Dynamical Systems, 2017, 37 (9) : 4753-4766. doi: 10.3934/dcds.2017204
[20]

Luiza H. F. Andrade, Rui F. Vigelis, Charles C. Cavalcante. A generalized quantum relative entropy. Advances in Mathematics of Communications, 2020, 14 (3) : 413-422. doi: 10.3934/amc.2020063

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (67)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy