Smooth chaotic 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.

A New Chaotic System with Positive Topological Entropy

This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are ...

On Topological Sequence Entropy and Chaotic Maps on Inverse Limit Spaces

The aim of this paper is to prove the following results: a continuous map f : [0, 1]→ [0, 1] is chaotic iff the shift map σf : lim ← ([0, 1], f)→ lim ← ([0, 1], f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. σf : lim ← ([0, 1], f) → lim ← ([0, 1], f) is chaotic iff there exists an increasing sequence of positive integers A such that the topological s...

Zero - Entropy Affine Maps on Homogeneous Spaces

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...