On dynamics of graph maps with zero topological entropy

Topological entropy on zero-dimensional spaces

Let X be an uncountable compact metrizable space of topological dimension zero. Given any a ∈ [0,∞] there is a homeomorphism on X whose topological entropy is a.

Zero - Entropy Affine Maps on Homogeneous Spaces

A Note on the Periodic Orbits and Topological Entropy of Graph Maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

On strongly Jordan zero-product preserving maps

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

TOPOLOGICAL ENTROPY OF m-FOLD MAPS

We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a C1 map has at least m preimages then the topological entropy of the map is at least log m. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at leas...