Related papers: Smooth Stable Foliations of Anosov Diffeomorphisms

The goal of this article is to establish several general properties of a somewhat large class of partially hyperbolic diffeomorphisms called \emph{discretized Anosov flows}. A general definition for these systems is presented and is proven…

We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006…

We apply the matching functions technique in the setting of contact Anosov flows which satisfy a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman-Ornstein~\cite{FO}. Namely, we show that if two…

In this paper we will show that if a sequence of natural numbers satisfies a certain growth rate, then there is a weak mixing diffeomorphism on $\mathbb{T}^2$ that is uniformly rigid with respect to that sequence. The proof is based on a…

We prove that a $C^2$-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the $C^2$-stability conjecture for Riemannian geodesic flows of closed…

This paper deals with random perturbations of diffeomorphisms on n-dimensional Riemannian manifolds with distributions supported on k-dimensional disks, where k<n. First we demonstrate general but not very intuitive conditions which…

We give new proofs of the K-polystability of two smooth Fano threefolds. One of them is a~smooth divisor in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,1)$, which is unique up to isomorphism. Another one is the~blow…

This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the…

We show that the set of singular holomorphic foliations of the projective spaces with split tangent sheaf and with good singular set is open in the space of holomorphic foliations. As applications we present a generalization of a result by…

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 show that the time-1 map of an Anosov flow, whose strong-unstable foliation is $C^2$ smooth and minimal, is $C^2$ close to a diffeomorphism having positive central Lyapunov exponent Lebesgue almost everywhere and a unique physical…

We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into…

We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…

Let $f\colon\mathbb{T}^d\to\mathbb{T}^d$ be an Anosov diffeomorphism whose linearization $A\in{\rm GL}(d,\mathbb{Z})$ is irreducible. Assume that $f$ is also absolutely partially hyperbolic where a weak stable subbundle is considered as the…

We study coisotropic deformations of a compact regular coisotropic submanifold $C$ in a contact manifold $(M,\xi)$. Our main result states that $C$ is rigid among nearby coisotropic submanifolds whose characteristic foliation is…

We exhibit a local residual set of surface $C^1$ diffeomorphisms that are continuum-wise expansive but are not expansive. We also exhibit an open and dense set of surface $C^1$ diffeomorphisms where expansiveness implies being Anosov.

We consider a smooth Anosov diffeomorphism with a smooth dynamical foliation. We show upper bounds on the essential spectral radius of its transfer operator acting on anisotropic Sobolev spaces. (Such bounds are related to the essential…

We prove that a transitive uniformly $u$-quasiconformal Anosov diffeomorphism with a two-dimensional unstable distribution has a globally defined stable holonomy. As a corollary, we are able to remove an additional assumption in a theorem…

Coboundary expansion (with $\mathbb{F}_2$ coefficients), and variations on it, have been the focus of intensive research in the last two decades. It was used to study random complexes, property testing, and above all Gromov's topological…

Given a $C^0$ conjugacy between two Anosov diffeomorphisms, the matching periodic data problem asks whether this conjugacy is smooth provided spectral data of the diffeomorphisms match at periodic points. We show that if the two $C^0$…