Related papers: Semiclassical measures for complex hyperbolic quot…

Determination of periodic orbits for a Hamiltonian system together with their semi-classical quantization has been a long standing problem. We consider here resonances for a $h$-Pseudo-Differential Operator $H(y,hD_y;h)$ induced by a…

We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic manifolds which are as aperiodic as…

We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supports coincide with the homoclinic class. Second, we show…

In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+\alpha}$ diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property…

In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs $u$-states are hyperbolic. We prove the finiteness of ergodic physical measures. Then…

Starting from the framework defined by Matveev and Shevchishin we derive the local and the global structure for the four types of super-integrable Koenigs metrics. These dynamical systems are always defined on non-compact manifolds, namely…

We prove the existence of Sinai-Ruelle-Bowen measures for a class of $C^2$ self-mappings of a rectangle with unbounded derivatives. The results can be regarded as a generalization of a well-known one dimensional Folklore Theorem on the…

In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to…

Using quadratic forms, we stablish a criteria to relate the curvature of a Riemannian manifold and partial hyperbolicity of its geodesic flow. We show some examples which satisfy the criteria and another which does not satisfy it but still…

We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensional bundle and there is a uniform lower bound for the absolute…

This paper presents a rigorous study of advanced functional spaces, with a focus on Sobolev and Besov spaces, to investigate key aspects of fluid dynamics, including the regularity of solutions to the Navier-Stokes equations, hypercomplex…

In this paper, we establish the spectral decomposition of the Koopman operator and determine the flat-trace distribution associated with the geodesic flow on the co-circle bundle over the compactification of Poincar\'e upper half-plane…

Using the works of Ma\~n\'e \cite{Ma} and Paternain \cite{Pat} we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a $\mathcal{C}^{\infty}$ Riemannian…

In this paper we prove that for an ergodic hyperbolic measure $\omega$ of a $C^{1+\alpha}$ diffeomorphism $f$ on a Riemannian manifold $M$, there is an $\omega$-full measured set $\widetilde{\Lambda}$ such that for every invariant…

We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case, with two recent infinite-volume…

Let $(M,g)$ be a complete non-compact Riemannian manifold together with a function $e^h$, which weights the Hausdorff measures associated to the Riemannian metric. In this work we assume lower or upper radial bounds on some weighted or…

In this paper, we address an extension of the theory of self-concordant functions for a manifold. We formulate the self-concordance of a geodesically convex function by a condition of the covariant derivative of its Hessian, and verify that…

We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also…

We obtain geometric lower bounds for the low Steklov eigenvalues of finite-volume hyperbolic surfaces with geodesic boundary. The bounds we obtain depend on the length of a shortest multi-geodesic disconnecting the surfaces into connected…

Hyperbolic monopole motion is studied for well separated monopoles. It is shown that the motion of a hyperbolic monopole in the presence of one or more fixed monopoles is equivalent to geodesic motion on a particular submanifold of the full…