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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

WoS  JIF 2026 : 0.5 (Q3)

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Research Article

ON APPROXIMATION OF RELATIVE ENTROPIES

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pp. 1–14Vol. 21Issue 1May 2023DOI: 10.47974/JDSGT-21-1-P02XML
Received:
02 Feb 2023
Published Online:
01 May 2023
Article type:
Research Article
Language:
EN
Article no.:
JDSGT-21-1-P02
Pages:
1–14

Abstract

We analyze when symbolic dynamical systems have intermediate relative entropies for two symbolic spaces (X, o1) and (Y, o2). By this is understood to study the denseness of relative measure-theoretic entropies in the interval [0, h(v, o1)], where h(v, o1) is a relative topological entropy of the shift o1 with respect to a o2-invariant measure  in Y . We prove that for irreducible shifts with the (strong) specification property as introduced by Bowen, the set of the relative measure-theoretic entropies is dense in the above mentioned sense. To this, we use the decomposition of factor codes of Yoo and a variational principle for relative entropies given by Barral and Feng.

Keywords

Relative entropiesMeasures of maximal entropySpecification propertyIrreducible shifts

Subject Classifications

37A3537B10

References

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[4] D.J. Feng, Equilibrium states for factor maps between subshifts, Adv. Math. 226 (2011) 2370-2502.
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[8] M. Li, Y. Shi, S. Wang and X. Wang, Measures of intermediate entropies for star vector  elds, Israel Journal of Mathematics, 240 (2020) 701-819.
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[10] P. Sun, Denseness of intermediate pressures for systems with the Climenhaga-Thompson structures, J. Math Anal Appl 487 (2020b) 4-17.
[11] J. Yoo, Decomposition of in nite-to-one factor codes and uniqueness of relative equilibrium states, J. Mod. Dynam., 13 (2018) 271-284.

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