相关论文: Attractors and Time Averages for Random Maps
The existence of quasimorphisms on groups of homeomorphisms of manifolds has been extensively studied under various regularity conditions, such as smooth, volume-preserving, and symplectic. However, in this context, nothing is known about…
In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…
We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for…
We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…
The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…
Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an…
We prove that $n$-sphere $\mathbb{S}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{S}^n\to\mathbb{S}^n$ with non-orientable expanding attractors of any topological dimension $d\in\{1,\ldots,[\frac{n}{2}]\}$ where $[x]$…
For any $1\le r\le \infty$, we show that every diffeomorphism of a manifold of the form $\mathbb{R}/\mathbb{Z} \times M$ is a total renormalization of a $C^r$-close to identity map. In other words, for every diffeomorphism $f$ of…
We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be close to a fixed map; thus, our results can…
In this work, we discuss the large time behavior of the solutions of the two dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations in bounded domains. Under the functional setting $\V\hookrightarrow\H\hookrightarrow\V'$,…
The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate…
We give a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions. This includes uniform energy-to-Strichartz estimates, the existence of uniform attractors in a weak or strong…
Given $k\in \mathbb{R},$ $v,$ $D>0,$ and $n\in \mathbb{N},$ let $\left\{ M_{\alpha }\right\} _{\alpha =1}^{\infty }$ be a Gromov-Hausdorff convergent sequence of Riemannian $n$--manifolds with sectional curvature $\geq k,$ volume $>v,$ and…
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these…
We uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps characterized each by a Lyapunov exponent that diverges to minus infinity. Amongst the main novel properties are the following: i) The…
Using a new and general method, we prove the existence of random attractor for the three dimensional stochastic primitive equations defined on a manifold $\D\subset\R^3$ improving the existence of weak attractor for the deterministic model.…
We show that at the vicinity of a generic dissipative homoclinic unfolding of a surface diffeomorphism, the Hausdorff dimension of the set of parameters for which the diffeomorphism admits infinitely many periodic sinks is at least 1/2.
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…
In this paper we continue to explore infinitely renormalizable H\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with…