14 citations · 27 across the 14 of their papers we have counts for
10 papers · 1 filter
Interval maps of given topological entropy and Sharkovskii's type
Sylvie Ruette
It is known that the topological entropy of a continuous interval map is positive if and only if the type of for Sharkovskii's order is for some odd integer $p\ge 3…
Periodic orbits of large diameter for circle maps
Lluís Alsedà, Sylvie Ruette
Let be a continuous circle map and let be a lifting of . In this note we study how the existence of a large orbit for affects its set of periods. More precisely, we…
Rotation set for maps of degree 1 on sun graphs
Sylvie Ruette
For a continuous map on a topological graph containing a unique loop S, it is possible to define the degree and, for a map of degree 1, rotation numbers. It is known that the set o…
Rotation sets for graph maps of degree 1
Lluís Alsedà, Sylvie Ruette
For a continuous map on a topological graph containing a loop it is possible to define the degree (with respect to the loop ) and, for a map of degree , rotation numbers.…
Large entropy implies existence of a maximal entropy measure for interval maps
Jérôme Buzzi, Sylvie Ruette
We give a new type of sufficient condition for the existence of measures with maximal entropy for an interval map , using some non-uniform hyperbolicity to compensate for a lack…
Transitive sensitive subsystems for interval maps
Sylvie Ruette
We state that for continuous interval maps the existence of a non empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topol…
Dense chaos for continuous interval maps
Sylvie Ruette
A continuous map from a compact interval into itself is densely (resp. generically) chaotic if the set of points such that …
On the Vere-Jones classification and existence of maximal measures for countable topological Markov chains
Sylvie Ruette
We consider topological Markov chains (also called Markov shifts) on countable graphs. We show that a transient graph can be extended to a recurrent graph of equal entropy which is…
Asymptotic pairs in positive-entropy systems
François Blanchard, Bernard Host, Sylvie Ruette
We show that in a topological dynamical system of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs such that and $\lim_{…
Mixing maps of the interval without maximal measure
Sylvie Ruette
We construct a transformation of the interval (or the torus) which is topologically mixing but has no invariant measure of maximal entropy. Whereas the assumption of $C^{\inf…