Weighted topological and measure-theoretic entropy

Tao Wang; Yu Huang

doi:10.3934/dcds.2019159

Article Contents

2019, Volume 39, Issue 7: 3941-3967. Doi: 10.3934/dcds.2019159

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Weighted topological and measure-theoretic entropy

Tao Wang and
Yu Huang^,

School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

^* Corresponding author: Yu Huang
^* Corresponding author: Yu Huang

Received: April 30, 2018

Revised: September 30, 2018

Published: April 2019

The second author is supported by National Nature Science Funds of China (11771459)

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Abstract

Feng and Huang in 2016 defined a new notion called weighted topological entropy (pressure) and obtained the corresponding variational principle for compact dynamical systems. In this paper, it was our hope to carry out a further study from the following three aspects:

(1) Inspired from the well-known classical entropy theory, we define various weighted topological (measure-theoretic) entropies and investigate their relationships.

(2) The classical entropy formula of subsets and their transformations by factor maps is generalized to the weighted version.

(3) A formula which comes from the Brin-Katok theorem of weighted conditional entropy is established.

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Mathematics Subject Classification: Primary: 37C45, 37B40, 37A35.

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