Sylvie Ruette

Asymptotic pairs in positive-entropy systems

We show that in a topological dynamical system

Comparison-based algorithms are robust and randomized algorithms are anytime

(X,T)

MixingCrmaps of the interval without maximal measure

of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs

Dense chaos for continuous interval maps

(x,y)

For graph maps, one scrambled pair implies Li-Yorke chaos

such that

PERIODIC ORBITS OF LARGE DIAMETER FOR CIRCLE MAPS

x\not= y

On the Vere–Jones classification and existence of maximal measures for countable topological Markov chains

and

Chaos on the Interval

\lim_{n\to +\infty} d(T^n x,T^n y)=0

ROTATION SETS FOR GRAPH MAPS OF DEGREE 1

. More precisely we consider a

Large entropy implies existence of a maximal entropy measure for interval maps

T