The topological entropy of iterated piecewise affine maps is uncomputable.
The Topological Entropy of the Transformation x ... ax (1-x).
The topological entropy versus level sets for interval maps
We answer affirmatively Coven's question [PC]: Suppose f: I → I is a continuous function of the interval such that every point has at least two preimages. Is it true that the topological entropy of f is greater than or equal to log 2?
The topological entropy versus level sets for interval maps (part II)
Let f: [a,b] → [a,b] be a continuous function of the compact real interval such that (i) for every y ∈ [a,b]; (ii) for some m ∈ ∞,2,3,... there is a countable set L ⊂ [a,b] such that for every y ∈ [a,b]∖L. We show that the topological entropy of f is greater than or equal to log m. This generalizes our previous result for m = 2.
The topology of holomorphic flows with singularity
The topology of integrable differential forms near a singularity
The Tribonacci substitution.
The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3
The uniform attractors for the nonhomogeneous 2D Navier-Stokes equations in some unbounded domain.
The uniqueness of invariant measures for Markov operators
It is shown that Markov operators with equicontinuous dual operators which overlap supports have at most one invariant measure. In this way we extend the well known result proved for Markov operators with the strong Feller property by R. Z. Khas'minski.
The universal minimal system for the group of homeomorphisms of the Cantor set
Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact noncompact group this is a nonmetrizable system with a rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one-point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizable space and for which one has an explicit description. We show that for the topological group G = Homeo(E) of self-homeomorphisms...
The vector individual weighted ergodic theorem for bounded Besicovich sequences.
The Weinstein conjecture in cotangent bundles and related results
The Weinstein Conjecture in P X Cl.
The Williams conjecture is false for irreducible subshifts.
The Williams conjecture is false for irreducible subshifts.
The zeta functions of Ruelle and Selberg. I
The -algebra of pasts of a random walk on the orbits of the Bernoulli action of the group .
Théorème de Kurosh pour les relations d’équivalence boréliennes
En théorie des groupes, le théorème de Kurosh est un résultat de structure concernant les sous-groupes d’un produit libre de groupes. Le théorème principal de cet article est un résultat analogue dans le cadre des relations d’équivalence boréliennes à classes dénombrables, que nous démontrons en développant une théorie de Bass-Serre dans ce cadre particulier.
Théorèmes ergodiques individuels purement topologiques