On topological sequence entropy and chaotic maps on inverse limit spaces.
On uniformly quasisymmetric groups of circle diffeomorphisms.
One dimensional dynamics and factors of finite automata
One-dimensional and two-dimensional dynamics of cubic maps.
-adic chaos and random number generation.
Parabolic Cantor sets
The notion of a parabolic Cantor set is introduced allowing in the definition of hyperbolic Cantor sets some fixed points to have derivatives of modulus one. Such difference in the assumptions is reflected in geometric properties of these Cantor sets. It turns out that if the Hausdorff dimension of this set is denoted by h, then its h-dimensional Hausdorff measure vanishes but the h-dimensional packing measure is positive and finite. This latter measure can also be dynamically characterized as the...
Plane affine geometry and Anosov flows
Pourquoi les points périodiques des homéomorphismes du plan tournent-ils autour de certains points fixes ?
Soit un homéomorphisme du plan qui préserve l’orientation et qui a un point périodique de période . Nous montrons qu’il existe un point fixe tel que le nombre d’enlacement de et ne soit pas nul. En d’autres termes, le nombre de rotation de l’orbite de dans l’anneau est un élément non nul de . Ceci donne une réponse positive à une question posée par John Franks.
Powers and alternative laws
A groupoid is alternative if it satisfies the alternative laws and . These laws induce four partial maps on
Puissance extérieure d'un automate déterministe, application au calcul de la fonction zêta d'un système sofique
Renormalization of cocycles and linear ODE with almost-periodic coefficients.
Rescaling of Markov shifts.
Rigidity and inflexibility in conformal dynamics.
Rigidity and renormalization in one dimensional dynamical systems.
Roots of continuous piecewise monotone maps of an interval.
Rotation sets for some non-continuous maps of degree one.
Rotation sets for subshifts of finite type
For a dynamical system (X,f) and a function the rotation set is defined. The case when (X,f) is a transitive subshift of finite type and φ depends on the cylinders of length 2 is studied. Then the rotation set is a convex polyhedron. The rotation vectors of periodic points are dense in the rotation set. Every interior point of the rotation set is a rotation vector of an ergodic measure.
Scaling in a map of the two-torus.
Self-Similar Sets 3. Constructions with Sofic Systems.
Sequences of fixed point indices of iterations in dimension 2.