Related papers: Generic non-trivial resonances for Anosov diffeomo…

(Revised version, January 2006. S. Gouezel pointed out that, when 1<r<2, the proof in the previous version was incomplete. In fixing this gap, we simplified the argument in Section 6. In addition, there is a new appendix, with an…

We consider perturbations of the non-unitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of non-integrable singularities in the resulting theories leads to constraints on the…

In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…

The Ruelle resonances of a dynamical system are spectral data describing the precise asymptotics of correlations. We classify them completely for a class of chaotic two-dimensional maps, the linear pseudo-Anosov maps, in terms of the action…

We study relations between non-commutative Ruelle transfer operators over the C$^*$-algebra $B(\mathcal{H})$ of linear bounded operators over separable Hilbert spaces $\mathcal{H}$ (infinite-dimensional) and other completely positive maps.…

In the present paper we consider a generic perturbation of a nearly integrable system of $n$ and a half degrees of freedom $ H_\epsilon(\theta,p,t)=H_0(p)+\epsilon H_1(\theta,p,t)$, with a strictly convex $H_0$. For $n=2$ we show that at a…

On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex…

The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…

For certain real analytic data, we show that the eigenvalue sequence of the associated transfer operator L is insensitive to the holomorphic function space on which L acts. Explicit bounds on this eigenvalue sequence are established.

In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$…

Faure and Tsujii recently proposed a new quantization theory for symplectic Anosov diffeomorphisms. It combines prequantization with the study of the Pollicott--Ruelle resonances of an associated transfer operator. We apply this framework…

For any pseudo-Riemannian hyperbolic space $X$ over $\mathbb{R},\mathbb{C},\mathbb{H}$ or $\mathbb{O}$, we show that the resolvent $R(z)=(\Box-z\operatorname{Id})^{-1}$ of the Laplace-Beltrami operator $-\Box$ on $X$ can be extended…

We study the holomorphic twist of 3d N = 2 supersymmetric field theories, discuss the perturbative bulk local operators in general, and explicitly construct non perturbative bulk local operators for abelian gauge theories. Our construction…

We answer a question of Burns and Wilkinson, showing that there are open families of volume-preserving partially hyperbolic diffeomorphisms which are accessible and center bunched and neither dynamically coherent nor Anosov. We also show in…

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to…

In this paper we construct some "pathological" volume preserving partially hyperbolic diffeomorphisms on $\toro{3}$ such that their behaviour in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their…

Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic…

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus,…