Related papers: Center manifolds for Random Dynamical Systems with…

We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the…

Stochastic invariant manifolds are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and smoothness of center manifolds for a class of stochastic…

Stochastic center manifolds theory are crucial in modelling the dynamical behavior of complex systems under stochastic influences. A multiplicative ergodic theorem on Hilbert space is proved to be satisfied to the exponential trichotomy…

The center manifold is useful for describing the long-term behavior of a system of differential equations. In this work, we consider an autonomous differential equation in a Banach space that has the exponential trichotomy property in the…

In a Banach space, assuming that a linear nonautonomous differential equation $v'=A(t)v$ admits a very general type of trichotomy, we establish conditions for the existence of global Lipschitz invariant center manifold of the perturbed…

We investigate the existence and regularity of locally invariant manifolds near an approximately invariant set that satisfies a geometric hyperbolicity condition with respect to an abstract ``generalized" dynamical system in Banach spaces.…

A general local center manifold theorem around stationary trajectories is proved for nonlinear cocycles acting on measurable fields of Banach spaces.

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of equations of motion, viewing motion as a curve in an infinite-dimensional Banach space of embeddings of a body manifold…

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…

In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original…

In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. We motivate our approach by illustrative examples.

The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…

The paper considers a general concept of dichotomy with different growth rates for linear discrete-time systems in Banach spaces. Characterizations in terms of Lyapunov type sequences of norms are given. The approach is illustrated by…

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…

In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization in terms of an appropriate admissibility property. These…

We give a proof of existence of centre manifolds within large domains for systems with an integral of motion. The proof is based on a combination of topological tools, normal forms and rigorous-computer-assisted computations. We apply our…

We consider perturbations of normally hyperbolic invariant manifolds, under which they can lose their hyperbolic properties. We show that if the perturbed map which drives the dynamical system exhibits some topological properties, then the…

The paper emphasizes asymptotic behaviors, as stability, instability, dichotomy and trichotomy for skew-evolution semiflows, defined by means of evolution semiflows and evolution cocycles and which can be considered generalizations for…

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…