L'entropie minimale des espaces symétriques
Lifting Measures to Markov Extensions.
Locally equicontinuous dynamical systems
A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems....
Logarithmic convexity of push-forward measures.
Logarithmic measures, subdimension and Lyapunov exponents of Cantori
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
Lyapunov exponents, KS-entropy and correlation decay in skew product extensions of Bernoulli endomorphisms
Viene considerata una classe di sistemi dinamici del toro bidimensionale . Tali sistemi presentano la forma di un prodotto skew fra l'endomorfismo Bernoulli , , definito sul toro undidimensionale ed una traslazione del toro stesso. Si dimostra che gli esponenti di Liapunov e l'entropia di Kolmogorov-Sinai della misura di Haar invariante possono essere calcolati esplicitamente. Viene infine discusso il decadimento delle correlazioni per i caratteri.
Measurable dynamics of -unimodal maps of the interval
Métriques à entropie topologique positive sur
Mild law of large numbers and its consequences
Minimal measures.
More Denjoy minimal sets for area preserving diffeomorphisms.
Multiple Rokhlin tower theorem: A simple proof.
Non singular transformations and spectral analysis of measures
Non-hyperbolicity and invariant measures for unimodal maps
Non-uniformly hyperbolic billiards
Note à propos d'un résultat de Kowada sur les flots analytiques
On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.
On a certain map of a triangle
The paper answers some questions asked by Sharkovski concerning the map F:(u,v) ↦ (u(4-u-v),uv) of the triangle Δ = u,v ≥ 0: u+v ≤ 4. We construct an absolutely continuous σ-finite invariant measure for F. We also prove the following strange phenomenon. The preimages of side I = Δ ∩ v=0 form a dense subset of Δ and there is another dense set Λ consisting of points whose orbits approach the interval I but are not attracted by I.
On a one-dimensional analogue of the Smale horseshoe
We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.