Related papers: Exponential mixing of frame flows for three dimens…

The aim of this paper is to establish exponential mixing of frame flow for the measure of maximal entropy on a convex cocompact hyperbolic manifold. Consequences include results on the decay of matrix coefficients and on effective…

We show that a topologically mixing $C^\infty$ Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential.

Let $M$ be a closed $3$-dimensional Riemann manifold and let $3\le r\le \infty$. We prove that there exists an open dense subset in the space of $C^r$ volume-preserving Anosov flows on $M$ such that all the flows in it are exponentially…

The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic…

On a compact manifold of any dimension $d\geq 3$, we show that joint non-integrability of the stable and unstable foliation of a hyperbolic attractor with one-dimensional expanding direction, for a vector field of class $C^2$, implies…

We prove that an Anosov flow with $\mathcal{C}^{1}$ stable bundle mixes exponentially whenever the stable and unstable bundles are not jointly integrable. This allows us to show that if a flow is sufficiently close to a volume-preserving…

We consider the advection equation on $\mathbb{T}^2$ with a real analytic and time-periodic velocity field that alternates between two Hamiltonian shears. Randomness is injected by alternating the vector field randomly in time between just…

We revisit the classical framework developed by Brin, Pesin and others to study ergodicity and mixing properties of isometric extensions of volume-preserving Anosov flows, using the microlocal framework developed in the theory of…

We introduce a family of hyperbolic flows on non-compact phase spaces that includes the geodesic flow on the modular surface. For these systems we prove exponential decay of correlations for sufficiently regular observables with respect to…

As a final work to establish that frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions are exponentially mixing with respect to the Bowen-Margulis-Sullivan measure, this paper focuses on the case with cusps. To…

We prove that the geodesic flow on a geometrically finite locally symmetric space of negative curvature is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure. The approach is based on constructing a suitable…

We establish exponential mixing for the geodesic flow $\varphi_t\colon T^1S\to T^1S$ of an incomplete, negatively curved surface $S$ with cusp-like singularities of a prescribed order. As a consequence, we obtain that the Weil-Petersson…

We performed a numerical study of the efficiency of mixing by alternating horizontal and vertical shear ``wedge'' flows on the two-dimensional torus. Our results suggest that except in cases where each individual flow is applied for only a…

Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models of laminar mixing which incorporate this feature and have proven mixing properties. Here we…

We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded…

For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension…

We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of $T^2 \times…

We consider the Teichmuller flow on the unit cotangent bundle of the moduli space of compact Riemann surfaces with punctures. We show that it is exponentially mixing for the Ratner class of observables. More generally, this result holds for…

Let $\Gamma$ be a Zariski dense convex cocompact subgroup contained in an arithmetic lattice of $\operatorname{SO}(n, 1)^{\circ}$. We prove uniform exponential mixing of the geodesic flow for congruence covers of the hyperbolic manifold…

Let $G$ be a connected center-free simple real algebraic group of rank one and $\Gamma < G$ be a Zariski dense torsion-free convex cocompact subgroup. We prove that the frame flow on $\Gamma \backslash G$, i.e., the right translation action…