Related papers: Anosov Flows and Dynamical Zeta Functions

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…

In this paper we consider the transfer operator approach to the Ruelle and Selberg zeta functions associated to continued fractions transformations and the geodesic flow on the full modular surface. We extend the results by Ruelle and Mayer…

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the…

Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…

We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an R-covered transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold admits a regulating, transverse…

We give a new proof of the existence of compact surfaces embedded in $R^3$ with Anosov geodesic flows. This proof starts with a non-compact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone…

We show that for a contact Anosov flow on a compact manifold $ M $, the solutions to $ \partial_t u + X u = \nu \Delta u $, $ \nu > 0 $, where $ X $ is the generator of the flow and $ \Delta $, a (negative) Laplacian for some Riemannian…

We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian $2$-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow…

We continue our study of symplectically flat bundles. We broaden the notion of symplectically flat connections on symplectic manifolds to $\zeta$-flat connections on smooth manifolds. These connections on principal bundles can be…

A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as principal S^1-orbibundles over integral symplectic orbifolds…

We give some simple conditions under which a group acting on a bifoliated plane comes from the induced action of a pseudo-Anosov flow on its orbit space. An application of the strategy is a less technical proof of a result of Barbot that…

For each natural number n, we construct an example of a graph manifold supporting at least n different Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction: we cut a geodesic flow…

We consider a magnetic flow without conjugate points on a closed manifold $M$ with generating vector field $\G$. Let $h\in C^{\infty}(M)$ and let $\theta$ be a smooth 1-form on $M$. We show that the cohomological equation \[\G(u)=h\circ…

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank~1. This conjecture has been proved by Z. Szab\'{o} \cite{Sz} for harmonic manifolds with compact universal cover. E. Damek…

For a surface semiflow that is a suspension of a \( C^{1+\alpha} \) expanding Markov interval map, we prove that, under the assumptions that the roof function is Lipschitz continuous and not cohomologous to a locally constant function, the…

We prove the existence of a discrete correlation spectrum for Morse-Smale flows acting on smooth forms on a compact manifold. This is done by constructing spaces of currents with anisotropic Sobolev regularity on which the Lie derivative…

We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show $\mathbb{S}^3$ does not admit conformally Anosov Reeb…

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…

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structure, plus countably many special…

The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric…