On some aspects of local thermodynamical formalism
Abstract
In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way that does not neglect the initial transient part of an orbit. We investigate the properties of this ``transient'' version, which we call translocal entropy, and compute it in terms of Lyapunov exponents for various dynamical systems. We also investigate how this adjustment affects measure-theoretic local (Brin-Katok) entropy and local pressure functions, generalizing some partial variation principles of Ma \& Wen.
Keywords
Cite
@article{arxiv.2412.04055,
title = {On some aspects of local thermodynamical formalism},
author = {Andrzej Bis and Henk Bruin},
journal= {arXiv preprint arXiv:2412.04055},
year = {2025}
}
Comments
Update after the version was accepted in Qualitative Theory of Dynamical Systems, but using our own version, nut with the journal's template etc