Related papers: Flow-independent Anisotropic space, and perturbati…
A divergence-free vector field satisfies the star property if any divergence-free vector field in some C1-neighborhood has all singularities and all periodic orbits hyperbolic. In this paper we prove that any divergence-free vector field…
We study the spectral properties of the Ruelle-Perron-Frobenius operator associated to an Anosov map on classes of functions with high smoothness. To this end we construct anisotropic Banach spaces of distributions on which the transfer…
We consider the problem of spectra for acoustic type of turbulence generated by shocks being randomly distributed in space. We show that for turbulence with a weak anisotropy such spectra have the same dependence in $k$-space as the…
We consider theoretically the effects of an applied uniform magnetic field on the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya layered quantum Heisenberg antiferromagnets. The first case is relevant for systems…
We show, using semiclassical measures and unstable derivatives, that a smooth vector field $X$ generating a contact Anosov flow on a $3$-dimensional manifold $\mathcal{M}$ has only finitely many Ruelle resonances in the vertical strips $\{…
In this paper we study some properties of anisotropic Orlicz and anisotropic Orlicz-Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give…
We provide abstract conditions which imply the existence of a robustly invariant neighbourhood of a global section of a fibre bundle flow. We then apply such a result to the bundle flow generated by an Anosov flow when the fibre is the…
The first half of this paper is concerned with the topology of the space $\AAA(M)$ of (not necessarily contact) Anosov vector fields on the unit tangent bundle $M$ of closed oriented hyperbolic surfaces $\Sigma$. We show that there are…
In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable…
The anisotropic London equations taking into account the normal currents are derived and applied to the problem of the surface impedance in the Meisner state of anisotropic materials. It is shown that the complex susceptibility of…
In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(\alpha,\beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the…
We consider conformal vector models which could play the role of a cosmological dark radiation component. We analyse the propagation of gravitational waves in the presence of this vector background and find a suppression in the tensor…
These notes are based on lectures given by the author at the Summer School on Teichm\"uller dynamics, mapping class groups and applications in Grenoble, France, in June 2018 and at the Oberwolfach Seminar on Anisotropic Spaces and their…
We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlations for Anosov contact flows. The bounds follow the…
General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic…
We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting…
We investigate under which assumptions the flow associated to autonomous planar vector fields inherits the Sobolev or BV regularity of the vector field. We consider nearly incompressible and divergence-free vector fields, taking advantage…
This paper develops a family of Hofer-like metrics ($\dAnV{V}$) on the space of Anosov vector fields $\An(M)$, providing dynamically relevant distances based on the cost of deformation paths using $\Ck{k}$ or Sobolev $\SobolevHk{k}$ norms.…
Macroscopic systems with continuous symmetries subjected to oscillatory fields have phases and transitions that are qualitatively different from their equilibrium ones. Depending on the amplitude and frequency of the fields applied,…
We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of…