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New approach to weighted topological entropy and pressure

Part of: Topological dynamics Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory Ergodic theory

Published online by Cambridge University Press:  28 January 2022

MASAKI TSUKAMOTO
MASAKI TSUKAMOTO*
Affiliation:
Department of Mathematics, Kyushu University, Moto-oka 744, Nishi-ku, Fukuoka 819-0395, Japan
*
e-mail: tsukamoto@math.kyushu-u.ac.jp
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Abstract

Motivated by fractal geometry of self-affine carpets and sponges, Feng and Huang [J. Math. Pures Appl. 106(9) (2016), 411–452] introduced weighted topological entropy and pressure for factor maps between dynamical systems, and proved variational principles for them. We introduce a new approach to this theory. Our new definitions of weighted topological entropy and pressure are very different from the original definitions of Feng and Huang. The equivalence of the two definitions seems highly non-trivial. Their equivalence can be seen as a generalization of the dimension formula for the Bedford–McMullen carpet in purely topological terms.

Keywords

dynamical systemweighted topological entropyweighted topological pressurevariational principleBedford–McMullen carpet

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 37B40: Topological entropy 37A35: Entropy and other invariants, isomorphism, classification 37C45: Dimension theory of dynamical systems
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 3 , March 2023 , pp. 1004 - 1034
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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