Statistics, yokes and symplectic geometry
Steepest descent method on a Riemannian manifold: the convex case.
Stochastic Banach principle in operator algebras
The classical Banach principle is an essential tool for the investigation of ergodic properties of Cesàro subsequences. The aim of this work is to extend the Banach principle to the case of stochastic convergence in operator algebras. We start by establishing a sufficient condition for stochastic convergence (stochastic Banach principle). Then we prove stochastic convergence for bounded Besicovitch sequences, and as a consequence for uniform subsequences.
Stochastic behavior above Feigenbaum's parameter value
Stochastic dynamical systems with weak contractivity properties II. Iteration of Lipschitz mappings
In this continuation of the preceding paper (Part I), we consider a sequence of i.i.d. random Lipschitz mappings → , where is a proper metric space. We investigate existence and uniqueness of invariant measures, as well as recurrence and ergodicity of the induced stochastic dynamical system (SDS) starting at x ∈ . The main results concern the case when the associated Lipschitz constants are log-centered. Principal tools are local contractivity, as considered in detail in Part I, the Chacon-Ornstein...
Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity
Consider a proper metric space and a sequence of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic...
Stochastic effects on biodiversity in cyclic coevolutionary dynamics
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner. Although the deterministic approach predicts (neutrally) stable coexistence of all species, for any finite population size, the intrinsic stochasticity unavoidably causes the eventual extinction of two of them.
Stochastic Stability in Some Chaotic Dynamical Systems.
Stochastic weak attractor for a dissipative Euler equation.
Stochastically perturbed allelopathic phytoplankton model.
Strategies for computation of Lyapunov exponents estimates from discrete data
The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed...
Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity
A long-time dynamic for granular materials arising in the hypoplastic theory of Kolymbas type is investigated. It is assumed that the granular hardness allows exponential degradation, which leads to the densification of material states. The governing system for a rate-independent strain under stress control is described by implicit differential equations. Its analytical solution for arbitrary inhomogeneous coefficients is constructed in closed form. Under cyclic loading by periodic pressure, finite...
Stretching the Oxtoby-Ulam Theorem
On a manifold X of dimension at least two, let μ be a nonatomic measure of full support with μ(∂X) = 0. The Oxtoby-Ulam Theorem says that ergodicity of μ is a residual property in the group of homeomorphisms which preserve μ. Daalderop and Fokkink have recently shown that density of periodic points is residual as well. We provide a proof of their result which replaces the dependence upon the Annulus Theorem by a direct construction which assures topologically robust periodic points.
Strict measure rigidity for unipotent subgroups of solvable groups.
Strictly ergodic patterns and entropy for interval maps.
Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers
A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.
Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles
This article is about almost reducibility of quasi-periodic cocycles with a diophantine frequency which are sufficiently close to a constant. Generalizing previous works by L.H. Eliasson, we show a strong version of almost reducibility for analytic and Gevrey cocycles, that is to say, almost reducibility where the change of variables is in an analytic or Gevrey class which is independent of how close to a constant the initial cocycle is conjugated. This implies a result of density, or quasi-density,...
Strong bifurcation loci of full Hausdorff dimension
In the moduli space of degree rational maps, the bifurcation locus is the support of a closed positive current which is called the bifurcation current. This current gives rise to a measure whose support is the seat of strong bifurcations. Our main result says that has maximal Hausdorff dimension . As a consequence, the set of degree rational maps having distinct neutral cycles is dense in a set of full Hausdorff dimension.
Strong cellularity and global asymptotic stability
Strong convergence of additive Multidimensional Continued Fraction algorithms