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Commutativity and non-commutativity of topological sequence entropy

Francisco Balibrea, Jose Salvador Cánovas Peña, Víctor Jiménez López (1999)

Annales de l'institut Fourier

In this paper we study the commutativity property for topological sequence entropy. We prove that if X is a compact metric space and f , g : X → X are continuous maps then h A ( f ∘ g ) = h A ( g ∘ f ) for every increasing sequence A if X = [ 0 , 1 ] , and construct a counterexample for the general case. In the interim, we also show that the equality h A ( f ) = h A ( f | ∩ n ≥ 0 f n ( X ) ) is true if X = [ 0 , 1 ] but does not necessarily hold if X is an arbitrary compact metric space.

Compacts connexes invariants par une application univalente

Emmanuel Risler (1999)

Fundamenta Mathematicae

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...

Computing explicitly topological sequence entropy: the unimodal case

Victor Jiménez López, Jose Salvador Cánovas Peña (2002)

Annales de l’institut Fourier

Let W ( I ) denote the family of continuous maps f from an interval I = [ a , b ] into itself such that (1) f ( a ) = f ( b ) ∈ { a , b } ; (2) they consist of two monotone pieces; and (3) they have periodic points of periods exactly all powers of 2 . The main aim of this paper is to compute explicitly the topological sequence entropy h D ( f ) of any map f ∈ W ( I ) respect to the sequence D = ( 2 m - 1 ) m = 1 ∞ .

Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets

Chris Good, Brian E. Raines (2006)

Fundamenta Mathematicae

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.

Critical portraits for postcritically finite polynomials

Alfredo Poirier (2009)

Fundamenta Mathematicae

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.

Currently displaying 61 – 80 of 433