Related papers: Homogeneous Real (2,3,5) Distributions with Isotro…

The density property for a Stein manifold X implies that the group of holomorphic diffeomorphisms of X is infinite-dimensional and, in a certain well-defined sense, as large as possible. We prove that if G is a complex semisimple Lie group…

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the…

A homogenization problem of infinite dimensional diffusion processes indexed by ${\mathbf Z}^d$ having periodic drift coefficients is considered. By an application of the uniform ergodic theorem for infinite dimensional diffusion processes…

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…

A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be…

We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.

We consider possibly singular rational projective k*-surfaces and provide an explicit description of the unit component of the automorphism group in terms of isotropy group orders and intersection numbers of suitable invariant curves. As an…

The standard treatment of impurities in metals assumes a homogeneous distribution of impurities. In this paper we study distributions that are inhomogeneous. We discuss in detail the "isotropic inhomogeneous scattering model" which takes…

Using a complex parametrisation of $su(2)$, we show a change of coordinates that maps the maximally symmetric rolling $(2,3,5)$-distribution to the flat Cartan distribution. This establishes the local equivalence between the maximally…

We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.

We construct diffeomorphisms in dimension $d\geq 2$ exhibiting $C^1$-robust heteroclinic tangencies.

We recall first some basic facts on weighted homogeneous functions and filtrations in the ring $A$ of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor…

Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We…

In this paper, we prove a sufficient and necessary condition for the transition probability distribution of a general, time-inhomogeneous linear SDE to possess a density function and study the differentiability of the density function and…

In this paper we classify countable locally finite-by-abelian groups up to coarse isomorphism. This classification is derived from a coarse classification of amenable shift-homogeneous metric spaces.

We consider invariant covariant derivatives on reductive homogeneous spaces corresponding to the well-known invariant affine connections. These invariant covariant derivatives are expressed in terms of horizontally lifted vector fields on…

We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum…

We study $2$-step nilpotent Lorentzian Lie groups $N$, which are naturally reductive with respect to a certain class of transitive subgroups of isometries. We describe the isotropy representation and prove that its fixed points give raise…

Moderately large numbers of transitive elliptic spreads are constructed in characteristic $2$ and dimension $\equiv $ 2 (mod 4).