arXiv subjects
Publications and source records attributed to Andrzej Biś.
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure functions determined by the system.
We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological entropy introduced by Hofmann and Stoyanov. We analyze its basic properties and its relation with the classical metric entropy. In the case of semigroup actions on compact metric spaces we compare the receptive metric entropy with the receptive topological entropy looking for a Variational Principle. With this aim we propose several characterizations of the receptive topological entropy. Finally we introduce a receptive local metric entropy inspired by a notion by Bowen generalized in the classical setting of amenable group actions by Zheng and Chen, and we prove partial versions of the Brin-Katok Formula and the local Variational Principle.
We show that the entropy of a finitely generated pseudogroup (resp., of a foliation of a compact Riemannian manifold) can be calculated by suitable counting separated pseudo-orbits (resp., pseudoleaves).