scholarly journals Smooth invariant manifolds in Banach spaces with nonuniform exponential dichotomy

2006 ◽  
Vol 238 (1) ◽  
pp. 118-148 ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls
Keyword(s):  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Invariant Manifolds ◽  
Nonuniform Exponential Dichotomy

scholarly journals Roughness of(ℤ+,ℤ-)-Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Nicolae Lupa
Keyword(s):  
Banach Spaces ◽  
Explicit Form ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
General Context ◽  
Boundedness Condition ◽  
Infinite Dimensional ◽  
Perturbed Equation ◽  
Nonuniform Exponential Dichotomy

In this paper we study the roughness of(ℤ+,ℤ-)-nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients.

scholarly journals Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 105
Author(s):  
Lokesh Singh ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Growth Rate ◽  
Invariant Manifold ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stable Manifold ◽  
Exponential Dichotomy ◽  
Delay Differential ◽  
Stable Invariant ◽  
Nonuniform Exponential Dichotomy

In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt).

scholarly journals Invariant manifolds for flows in Banach spaces

1988 ◽  
Vol 74 (2) ◽  
pp. 285-317 ◽  
Author(s):  
Shui-Nee Chow ◽  
Kening Lu
Keyword(s):  
Banach Spaces ◽  
Invariant Manifolds

Ground States and Singular Ground States for Quasilinear Partial Differential Equations with Critical Exponent in the Perturbative Case

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Matteo Franca ◽  
Russell Johnson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Dichotomy ◽  
Invariant Manifolds ◽  
Ground States ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Quasilinear Partial Differential Equations ◽  
Melnikov Functions ◽  
The Family

AbstractWe study the structure of the family of radially symmetric ground states and singular ground states for certain elliptic partial differential equations with p- Laplacian. We use methods of Dynamical systems such as Melnikov functions, invariant manifolds, and exponential dichotomy.

NONUNIFORM EXPONENTIAL BEHAVIOUR AND TOPOLOGICAL EQUIVALENCE

2015 ◽  
Vol 58 (2) ◽  
pp. 279-291
Author(s):  
LUIS BARREIRA ◽  
LIVIU HORIA POPESCU ◽  
CLAUDIA VALLS
Keyword(s):  
Asymptotic Behaviour ◽  
Ergodic Theory ◽  
Canonical Form ◽  
Exponential Dichotomy ◽  
Topological Equivalence ◽  
Exponential Dichotomies ◽  
Exponential Behaviour ◽  
Nonuniform Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomy ◽  
Topological Conjugacies

AbstractWe show that any evolution family with a strong nonuniform exponential dichotomy can always be transformed by a topological equivalence to a canonical form that contracts and/or expands the same in all directions. We emphasize that strong nonuniform exponential dichotomies are ubiquitous in the context of ergodic theory. The main novelty of our work is that we are able to control the asymptotic behaviour of the topological conjugacies at the origin and at infinity.

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

Sign in / Sign up

Export Citation Format

Share Document