MIXED SPECTRUM REPARAMETERIZATIONS OF LINEAR FLOWS ON T 2 (2009)
Bassam Fayad, Anatole Katok, Alistar Windsor, Andrei Nikolaevich Kolmogorov, Ivan Georgievich Petrovskii
To the memory of great mathematicians of the 20th century,
UNIVERSITÀ DI PISA Ecole Doctorale de Sciences Mathématiques de Paris Centre (2008)
Doctorat En Informatique, Stefano Galatolo, Olivier Bournez, Abbas Edalat, Peter Gács, Olivier Bournez, ...
Mathieu HOYRUP Calculabilité, aléatoire et théorie ergodique sur les espaces métriques Calcolabilità, aleatorio e teoria ergodica in spazi metrici Thèse dirigée par
Nonstandard Smooth Realizations of Liouville Rotations (2006)
Fayad, Bassam, Saprykina, Maria, Windsor, Alistair
We augment the method of $C^\infty$ conjugation approximation with explicit estimates on the conjugacy map. This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically...
Smooth linearization of commuting circle diffeomorphisms (2006)
Fayad, Bassam, Khanin, Kostantin
We show that a finite number of commuting diffeomorphisms with simultaneously Diophantine rotation numbers are smoothly conjugated to roations.
Smooth mixing flows with purely singular spectra (2006)
We give a geometric criterion that implies a singular maximal spectral type for a dynamical system on a Riemannian manifold. The criterion, which is based on the existence of fairly rich but...
Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for SL(2,R) cocycles (2005)
We consider the linear cocycle $(T,A)$ induced by a measure preserving dynamical system $T:X \to X$ and a map $A:X \to \mathit{SL}(2,\mathbb{R})$. We address the dependence of the upper Lyapunov...
On the ergodicity of the Weyl sums cocycle (2005)
For $\theta \in [0,1]$, we consider the map $T_\a: \T^2 \to \T^2$ given by $T_\theta(x,y)=(x+\theta,y+2x+\theta)$. The skew product $f_\a: \T^2 \times \C \to \T^2 \times \C$ given by...
On the ergodicity of cylindrical transformations given by the logarithm (2005)
Fayad, Bassam, Lemańczyk, Mariusz
Given $\a \in [0,1]$ and $\varphi: \T \to \R$ measurable, the {\it cylindircal cascade} $S_{\a,\varphi}$ is the map from $\T \times \R$ to itself given by $S_{\a,\varphi} (x,y) = (x+\a,y+\varphi(x))$...
Fayad, Bassam, Saprykina, Maria
Let $M$ be an $m$-dimensional differentiable manifold with a nontrivial circle action ${\mathcal S}= {\lbrace S_t \rbrace}_{t \in\RR}, S_{t+1}=S_t$, preserving a smooth volume $\mu$. For any...
Constructions in elliptic dynamics (2005)
We present an overview and some new applications of the approximation by conjugation method introduced by Anosov and the second author more than thirty years ago \cite{AK}. Michel Herman made...
Fayad, Bassam, Windsor, Alistair
We provide sufficient conditions on a positive function so that its associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow.
Two remarks on the Shrinking Target Property (2005)
We show that a translation of vector V on the torus has the monotone shrinking target property if and only if the vector V is of constant type. Then, using reparametrizations of linear flows, we show...
Smooth mixing flows with singular spectra (2004)
We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but...
Smooth mixing flows with singular spectra (2004)
We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but...
Smooth mixing flows with singular spectra (2004)
We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but...
Rank one and mixing differentiable flows (2004)
We construct, over some minimal translations of the two torus, special flows under a differentiable ceiling function that combine the properties of mixing and rank one.
A remark on conservative diffeomorphisms (2004)
Bochi, Jairo, Fayad, Bassam, Pujals, Enrique
We show that a stably ergodic diffeomorphism can be $C^1$ approximated by a diffeomorphism having stably non-zero Lyapunov exponents.
Non uniform hyperbolicity and elliptic dynamics (2004)
We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.
Continuous spectrum on laminations over Aubry-Mather sets (2004)
If we perturb a completely integrable Hamiltonian system with two degrees of freedom, the perturbed flow might display, on every energy level, invariant sets that are laminations over Aubry-Mather...
Smooth mixing flows with singular spectra (2004)
We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but...
Smooth mixing flows with singular spectra (2004)
We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but...