Related papers: Higher order almost automorphy, recurrence sets an…

We develop a new framework to study minimum $d$-degree conditions in $k$-uniform hypergraphs, which guarantee the existence of a tight Hamilton cycle. Our main theoretical result deals with the typical absorption, path cover and connecting…

In the present work, for $\mathbb{X}$ a Banach space, the notion of piecewise continuous $\mathbb{Z}$-almost automorphic functions with values in finite dimensional spaces is extended to piecewise continuous $\mathbb{Z}$-almost automorphic…

Consider a dynamical system $T:\mathbb{T}\times \mathbb{R}^{d} \rightarrow \mathbb{T}\times \mathbb{R}^{d} $ given by $ T(x,y) = (E(x), C(y) + f(x))$, where $E$ is a linear expanding map of $\mathbb{T}$, $C$ is a linear contracting map of…

We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…

We consider again the fast-slow motions setups in the continuous time $\frac {dX_N(t)}{dt}=N^{1/2} \sig(X_N(t))(\xi(tN))+b(X_N(t)),\, t\in [0,T]$ and the discrete time $X_N((n+1)/N)=X_N(n/N)+N^{-1/2}\sig(X_N(n/N))\xi(n)+N^{-1}b(X_N(n/N)),\,…

This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of…

This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear…

Let $O$ be a complete d.v.r. and $G$ a finite group. We give two applications of an adjunction in the stable category of $OG$. The first application gives necessary and sufficient conditions for the middle term of an almost split sequence…

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…

We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…

This paper deals with random dynamical systems of polynomial automorphisms (complex generalized H\'{e}non maps and their conjugate maps) of $\Bbb{C}^{2}.$ We show that a generic random dynamical system of polynomial automorphisms has ``mean…

A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed…

This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory…

Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…

Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…

For Cartan geometries admitting automorphisms with isotropies satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open subset of the geometry with trivial holonomy. This…

We study the local regularity of sliding almost minimal sets of dimension 2 in $R^n$ , bounded by a smooth curve $L$. These are a good way to model soap films bounded by a curve, and their definition is similar to Almgren's. We aim for a…

Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…

We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption…

We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural discrete analogues of these sets and analyze their…