Exponential dichotomy of solutions of impulse systems

1989 ◽  
Vol 41 (6) ◽  
pp. 668-672 ◽  
Author(s):  
V. E. Slyusarchuk
Keyword(s):  
Exponential Dichotomy

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 On Exponential Dichotomy of Variational Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Bogdan Sasu
Keyword(s):  
Difference Equations ◽  
Exponential Dichotomy ◽  
New Method ◽  
Skew Product ◽  
Skew Product Flows

We give very general characterizations for uniform exponential dichotomy of variational difference equations. We propose a new method in the study of exponential dichotomy based on the convergence of some associated series of nonlinear trajectories. The obtained results are applied to difference equations and also to linear skew-product flows.

Admissible perturbations of exponential dichotomy roughness

1998 ◽  
Vol 31 (5-6) ◽  
pp. 559-571 ◽  
Author(s):  
Raúl Naulin ◽  
Manuel Pinto
Keyword(s):  
Exponential Dichotomy

Nonuniform Hyperbolicity and Admissibility

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls ◽  
Davor Dragičevič
Keyword(s):  
Exponential Dichotomy ◽  
Linear Operators ◽  
Nonuniform Hyperbolicity

AbstractFor a nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility in pairs of spaces (ℓ

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