We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties. We also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to C-dynamics.

For any C ∈ [0,∞] a compact group automorphism T : X → X is constructed with the property that 1 n log |{x ∈ X | T n(x) = x}| −→ C. This may be interpreted as a combinatorial analogue of the (still open) problem of whether compact group automorphisms exist with any given topological entropy.

It is shown that a piecewise affine area-preserving homeomorphism of the 2-torus studied by Cerbelli and Giona is pseudo-Anosov. This enables one to prove various of their conjectures and compute its topological entropy.

In this paper we give a brief view on the topological entropy. The results here presented are well known to the people working in the area, so this survey is mainly for non–experts in the field.

We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties. We also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to C-dynamics.

The aim of this paper is to extend the notion of topological entropy for fuzzy semidynamical systems created by a self-map on a fuzzy metric space. We show that if a metric space has two uniformly equivalent metrics, then fuzzy entropy is a constant up to these two metrics. We present a method to construct chaotic fuzzy semidynamical systems with arbitrary large fuzzy entropy. We also prove tha...

We prove formulae relating the topological entropy of a magnetic flow to the growth rate of the average number of trajectories connecting two points.