14 citations · 27 across the 14 of their papers we have counts for
15 papers
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…
Topological Markov chains of given entropy and period with or without measure of maximal entropy
Sylvie Ruette
We show that, for every positive real number h and every positive integer p, there exist oriented graphs G, G' (with countably many vertices) that are strongly connected, of period…
Chaos on the interval - a survey of relationship between the various kinds of chaos for continuous interval maps
Sylvie Ruette
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were…
On the set of periods of sigma maps of degree 1
Lluís Alsedà, Sylvie Ruette
We study the set of periods of degree 1 continuous maps from sigma into itself, where sigma denotes the space shaped like the letter sigma (i.e., a segment attached to a circle by…
For graph maps, one scrambled pair implies Li-Yorke chaos
Sylvie Ruette, L'ubomír Snoha
For a dynamical system , being a compact metric space with metric and being a continuous map , a set is scrambled if every pair of…
Rotation set for maps of degree 1 on the graph sigma
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 of…