Related papers: Dynamical systems method and a homeomorphism theor…

We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of…

The dynamical degree of a dominant rational map $f:\mathbb{P}^N\rightarrow\mathbb{P}^N$ is the quantity $\delta(f):=\lim(\text{deg} f^n)^{1/n}$. We study the variation of dynamical degrees in 1-parameter families of maps $f_T$. We make a…

Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb…

Consider a dynamical system $u \mapsto x, \dot{x} = f_{nl}(x,u)$ where $f_{nl}$ is a nonlinear (convex or nonconvex) function, or a combination of nonlinear functions that can eventually switch. We present, in this preliminary work, a…

One of the main problems of the theory of dynamical systems is the determination of the existence of periodic orbits of a self-map and more generally, the structure of the set of periods. Define the minimum period of a class os self-maps of…

Let S be a compact connected surface and let f be an element of the group Homeo\_0(S) of homeomorphisms of S isotopic to the identity. Denote by \tilde{f} a lift of f to the universal cover of S. Fix a fundamental domain D of this universal…

In this paper we prove some linking theorems and mountain pass type results for dynamical systems in terms of local semiflows on complete metric spaces. Our results provide an alternative approach to detect the existence of compact…

We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

Let $(W,\Pi)$ be a Riemann domain over a complex manifold $M$ and $w_0$ be a point in $W$. Let $\mathbb D$ be the unit disk in $\mathbb C$ and $\mathbb T=\bd\mathbb D$. Consider the space ${\mathcal S}_{1,w_0}({\bar{\mathbb D}},W,M)$ of…

Paper withdrawn; will be replaced by revised version containing application to lattice models as well. We study hierarchical properties of Sturmian words. These properties are similar to those of substitution dynamical systems. This…

Let $f$ be a homeomorphism of the closed annulus $A$ isotopic to the identity, and let $X\subset {\rm Int}A$ be an $f$-invariant continuum which separates $A$ into two domains, the upper domain $U_+$ and the lower domain $U_-$. Fixing a…

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 present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for…

If F is a type-definable family of commensurable subsets, subgroups or sub-vector spaces in a metric structure, then there is an invariant subset, subgroup or sub-vector space commensurable with F. This in particular applies to…

We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs $f\colon (X,x_0)\to (X,x_0)$, where $X$ is a complex surface having $x_0$ as a normal singularity. We prove that as long as $x_0$…

Let k be an algebraically closed field of characteristic 0, let X=P^1\times A^N and let f be a rational endomorphism of X given by (x,y)--->(g(x), A(x)y), where g is a rational function, while A is an N-by-N matrix with entries in k(x). We…

For a C^{1+\alpha} diffeomorphism f preserving a hyperbolic ergodic SRB measure \mu, Katok's remarkable results assert that \mu can be approximated by a sequence of hyperbolic sets \{\Lambda_n\}_{n\geq1}. In this paper, we prove the…

We study the space $H(\SO)$ of all homomorphisms of the vector lattice of all slowly oscillating functions on the half-line $\HH=[0,\infty)$. In contrast to the case of homomorphisms of uniformly continuous functions, it is shown that a…