Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Some new examples of recurrence and non-recurrence sets for products of rotations on the unit circle
We study recurrence and non-recurrence sets for dynamical systems on compact spaces, in particular for products of rotations on the unit circle . A set of integers is called -Bohr if it is recurrent for all products of rotations on , and Bohr if it is recurrent for all products of rotations on . It is a result due to Katznelson that for each there exist sets of integers which are -Bohr but not -Bohr. We present new examples of -Bohr sets which are not Bohr, thanks to a construction which...
Some qualitative features of turbulent mixing for far from equilibrium phenomena.
Some remarks on recent results about S-unimodal maps
Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number
We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]).
Spaces of ω-limit sets of graph maps
Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.
Stability of rotation pairs of cycles for the interval maps.
Stable and non-stable non-chaotic maps of the interval
Stable intersections of Cantor sets and homoclinic bifurcations
Statistical properties of unimodal maps
We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition...
Strictly ergodic patterns and entropy for interval maps.
Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles
This article is about almost reducibility of quasi-periodic cocycles with a diophantine frequency which are sufficiently close to a constant. Generalizing previous works by L.H. Eliasson, we show a strong version of almost reducibility for analytic and Gevrey cocycles, that is to say, almost reducibility where the change of variables is in an analytic or Gevrey class which is independent of how close to a constant the initial cocycle is conjugated. This implies a result of density, or quasi-density,...
Strong stochastic stability and rate of mixing for unimodal maps
Strong Transitivity and Graph Maps
We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.
Structure of Brouwer homeomorphismus. (Structure des homéomorphismes de Brouwer.)
Structure of inverse limit spaces of tent maps with finite critical orbit
Using methods of symbolic dynamics, we analyze the structure of composants of the inverse limit spaces of tent maps with finite critical orbit. We define certain symmetric arcs called bridges. They are building blocks of composants. Then we show that the folding patterns of bridges are characterized by bridge types and prove that there are finitely many bridge types.
Structure of one-dimensional chain-recurrent sets of flows on the 2-sphere and on the plane.
Substitution dynamical systems : algebraic characterization of eigenvalues
Substitutions and 1/2-discrepancy of nθ + x
Substitutions on two letters, cutting segments and their projections
In this paper we study the structure of the projections of the finite cutting segments corresponding to unimodular substitutions over a two-letter alphabet. We show that such a projection is a block of letters if and only if the substitution is Sturmian. Applying the procedure of projecting the cutting segments corresponding to a Christoffel substitution twice results in the original substitution. This induces a duality on the set of Christoffel substitutions.