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 variational principles of Ma & Wen.