Related papers: Smooth rigidity for codimension one Anosov flows

For a nonlinear Anosov diffeomorphism of the 2-torus, we present examples of measures so that the group of $\mu$-preserving diffeomorphisms is, up to zero-entropy transformations, cyclic. For families of equilibrium states $\mu$, we…

We obtain a fundamental measure density functional for mixtures of parallel hard cylinders. To this purpose we first generalize to multicomponent mixtures the fundamental measure functional proposed by Tarazona and Rosenfeld for a…

We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove…

We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a C2- open domain in the space of dynamical systems with a…

The leafwise cohomology of the weak stable foliation of the geodesic flows is very important in the study of the space of actions whose orbit foliation is the weak stable foliation of geodesic flows.The dimension one cohomology was computed…

We prove that if the stable foliation and the unstable foliation of an Anosov diffeomorphism on a connected compact manifold are $C^3$, then the diffeomorphism has fixed points. This is a partial positive answer to a Smale conjecture for…

Let $f,g$ be $C^2$ expanding maps on the circle which are topologically conjugate. We assume that the derivatives of $f$ and $g$ at corresponding periodic points coincide for some large period $N$. We show that $f$ and $g$ are…

In this paper we show that the geodesic flow of a Finsler metric is Anosov if and only if there exists a $C^2$ open neighborhood of Finsler metrics all of whose closed geodesics are hyperbolic. For surfaces this result holds also for…

We discuss several counterexamples to a rigidity conjecture of K. Khanin, which states that under some quantitative condition on non-existence of periodic orbits, $C^0$ conjugacy implies $C^1$ (even $C^\infty$) conjugacy. We construct…

We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, the $C^0$ norm of the derivative, and the Hofer/spectral norm. We obtain as a consequence that sufficiently fast convergence in Hofer/spectral…

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and discuss a framework to use tools from contact and symplectic geometry and topology in the study of Anosov dynamics. We also discuss some…

By carrying out a point-wise estimate for the second fundamental form, we prove a rigidity theorem of complete noncompact ancient solutions to the mean curvature flow in codimension one. Moreover, we derive an optimal growth condition.

Let $f\colon M\to M$ be an expansive homeomorphism with dense topologically hyperbolic periodic points, $M$ a compact manifold. Then there is a local product structure in an open and dense subset of $M$. Moreover, if some topologically…

We develop a "local theory" of multidimensional quasiperiodic $\SL(2,\R)$ cocycles which are not homotopic to a constant. It describes a $C^1$-open neighborhood of cocycles of rotations and applies irrespective of arithmetic conditions on…

We consider classes of partially hyperbolic diffeomorphism $f:M\to M$ with splitting $TM=E^s\oplus E^c\oplus E^u$ and $\dim E^c=2$. These classes include for instance (perturbations of) the product of Anosov and conservative surface…

In light of the rich results of expansiveness in the dynamics of diffeomorphisms, it is natural to consider another notions of expansiveness such as countably-expansive, measure expansive, $N$-expansive and so on. In this paper, we…

Given $\alpha$ in some set $\Sigma$ of total (Haar) measure in ${\bf T}={\bf R}/{\bf Z}$, and $A\in C^{\infty}({\bf T},SL(2,{\bf R}))$ which is homotopic to the identity, we prove that if the fibered rotation number of the skew-product…

We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar…

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a…

We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit…