Related papers: Self-adjoint Laplacians and symmetric diffusions o…

Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa--Holm equations are well-studied examples.A beautiful approach to well-posedness is…

Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum under various assumptions on the behavior of the magnetic…

We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency…

We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms $f$ on compact $3$-manifolds with fundamental groups of exponential growth such that $f^n$ is not homotopic to identity for all $n>0$.…

We consider a generic symplectic partially hyperbolic diffeomorphism close to direct/skew products of symplectic Anosov diffeomorphisms with area-preserving diffeomorphisms and prove that every hyperbolic periodic point has transverse…

The Grushin plane serves as one of the simplest examples of a sub-Riemannian manifold whose distribution is of non-constant rank. Despite the fact that the singular set where this distribution drops rank is itself a smoothly embedded…

We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L\'{e}vy index $\alpha $. The model applies to…

For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is…

We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms.

Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and $Y=[1,\infty)\times S^{1}$. We consider a family of complete surfaces arising by endowing $X\cup_{S^{1}}Y$ with a parameter dependent Riemannian metric, such that the…

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…

We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional,…

Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We…

The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkaehler 4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of the Thomas conjecture on existence of special Lagrangian representatives of…

The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…

We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of…

This article addresses the issue of uniform measure attractors for non-autonomous McKean-Vlasov stochastic reaction-diffusion equations defined on unbounded thin domains. Initially, the concept of uniform measure attractors is recalled, and…

An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group $G$, criteria for the existence of $G$-invariant self-adjoint extensions of…

We consider isotropic L\'evy processes on a compact Riemannian manifold, obtained from an $\mathbb{R}^d$-valued L\'evy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to…

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…