Related papers: Cohomological equations for suspension flows over …

In the current note we extend results by Marmi, Moussa and Yoccoz about cohomological equations for interval exchange transformations to irreducible linear involutions.

An asymptotic expansion is established for time averages of translation flows on flat surfaces. This result, which extends earlier work of A.Zorich and G.Forni, yields limit theorems for translation flows. The argument, close in spirit to…

We introduce notions of suspension and flow equivalence on one-sided topological Markov shifts, which we call one-sided suspension and one-sided flow equivalence, respectively. We prove that one-sided flow equivalence is equivalent to…

In this paper we present a proof of the Verjovsky conjecture: Every codimension-one Anosov flow on a manifold of dimension greater than three is topologically equivalent to the suspension of a hyperbolic toral automorphism. In fact, the…

We study the twisted cohomoligical equation over the geodesic flow on $SL(2,\mathbb{R})/\Gamma$. We characterize the obstructions to solving the twisted cohomological equation, construct smooth solution and obtain the tame Sobolev estimates…

We prove by methods of harmonic analysis a result on existence of solutions for twisted cohomological equations on translation surfaces with loss of derivatives at most 3+ in Sobolev spaces. As a consequence we prove that product…

Continuing the research initiated in \cite{Fr-Ki2}, we study the existence of solutions and their regularity for the cohomological equations $X u=f$ for locally Hamiltonian flows (determined by the vector field $X$) on a compact surface $M$…

We refine the theory of the cohomological equation for translation flows on higher genus surfaces with the goal of proving optimal results on the Sobolev regularity of solutions and of distributional obstructions. For typical translation…

In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem…

Following recent work of T. Alazard and C. Shao on applications of para-differential calculus to smooth conjugacy and stability problems for Hamiltonian systems, we prove finite codimension stability of invariant surfaces (in finite…

A geometric flow on $(2,2)$-forms is introduced which preserves the balanced condition of metrics, and whose stationary points satisfy the anomaly equation in Strominger systems. The existence of solutions for a short time is established,…

We show that any topologically transitive codimension-one Anosov flow on a closed manifold is topologically equivalent to a smooth Anosov flow that preserves a smooth volume. By a classical theorem due to Verjovsky, any higher dimensional…

We are motivated by a conjecture of A. and S. Katok to study the smooth cohomologies of a family of Weyl chamber flows. The conjecture is a natural generalization of the Livshitz Theorem to Anosov actions by higher-rank abelian groups; it…

We study the cohomological equation $Xu=f$ for smooth locally Hamiltonian flows on compact surfaces. The main novelty of the proposed approach is that it is used to study the regularity of the solution $u$ when the flow has saddle loops,…

In the present paper we give a positive answer to some questions posed by Viana on the existence of positive Lyapunov exponents for Hamiltonian linear differential systems. We prove that there exists an open and dense set of Hamiltonian…

We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…

Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno, Silva and Ruffino ($Stoch$. $Dyn$., 2013) it is shown that, up to a stopping time $\tau$, a stochastic flow of local…

We prove the existence of solutions of the cohomological equation for the geodesic flow on the unit tangent bundle of a compact flat surface with finitely many cone points. We also prove the ergodicity of the holonomy foliation for surfaces…

Impulse formulations of the Euler (and Navier-Stokes) equations were considered by Kuz'min [1] and Oseledets [2] and different impulse formulations are produced by various gauge transformations (Russo and Smereka[3]). The extension of the…

This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…