In this paper we study the commutativity property for topological sequence entropy. We prove that if is a compact metric space and are continuous maps then for every increasing sequence if , and construct a counterexample for the general case. In the interim, we also show that the equality is true if but does not necessarily hold if is an arbitrary compact metric space.
Let K be a compact connected subset of cc, not reduced to a point, and F a univalent map in a neighborhood of K such that F(K) = K. This work presents a study and a classification of the dynamics of F in a neighborhood of K. When ℂ K has one or two connected components, it is proved that there is a natural rotation number associated with the dynamics. If this rotation number is irrational, the situation is close to that of “degenerate Siegel disks” or “degenerate Herman rings” studied by R. Pérez-Marco...
We combine some results from the literature to give examples of completely mixing interval maps without limit measure.
Let denote the family of continuous maps from an interval into itself such that (1) ; (2) they consist of two monotone pieces; and (3) they have periodic points of periods exactly all powers of . The main aim of this paper is to compute explicitly the topological sequence entropy of any map respect to the sequence .
We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
We extend the work of Bielefeld, Fisher and Hubbard on critical portraits to arbitrary postcritically finite polynomials. This gives the classification of such polynomials as dynamical systems in terms of their external ray behavior.