Results 241 to 250 of about 42,543 (276)

Exponential Dichotomies by Ekeland’s Variational Principle

Journal of Dynamics and Differential Equations, 2020
Exponential dichotomy, which is a type of hyperbolicity in the context of linear time-varying systems, is the central focus of this paper. First, two well known characterizations of the exponential dichotomy in \(\mathbb{R}^+\) are presented: \begin{itemize} \item [(i)] If the system \(\dot{v}=A(t)v+f(t)\) in \(\mathbb{R}^N\), admits a bounded solution
Juan Campos, Massimo Tarallo
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Nonuniform Exponential Dichotomies and Lyapunov Regularity

Journal of Dynamics and Differential Equations, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barreira, Luis, Valls, Claudia
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Nonuniform exponential dichotomies and Lyapunov functions

Regular and Chaotic Dynamics, 2017
For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly ...
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
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Characterization of strong exponential dichotomies

Bulletin of the Brazilian Mathematical Society, New Series, 2015
We introduce the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. The latter refers to the exis- tence of (unique) bounded solutions for any bounded perturbation of the original dynamics. We consider the general case of a nonautonomous dy- namics
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
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Exponential Dichotomies: Discrete Time

2018
In this chapter we start discussing the admissibility theory in the general case of exponential dichotomies. The objective is the same—to characterize the notion of an exponential dichotomy in terms of an admissibility property. The arguments build substantially on those in Chapter 2, although there are various technical difficulties that need to be ...
Luís Barreira, Davor Dragičević, Claudia Valls   +2 more
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Exponential Dichotomies: Continuous Time

2018
This chapter is dedicated to the study of the admissibility theory for exponential dichotomies in continuous time. Again, the arguments build on those in Chapter 2, up to substantial technical complications. To the possible extent, we follow the path of Chapter 3.
Luís Barreira, Davor Dragičević, Claudia Valls   +2 more
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Smooth robustness of exponential dichotomies

Proceedings of the American Mathematical Society, 2011
The paper deals with the nonautonomous linear equation \(v_{m+1}=A_{m} v_{m}+B_{m}\left( \lambda\right) v_{m},\) where \(\lambda\) is a parameter in some open subset \(Y\) of a Banach space and where the function \(\lambda\mapsto B_{m}\left( \lambda\right) \) is of class \(C^{1},\) for all \(m\in\mathbb{Z}\).
Barreira, Luis, Valls, Claudia
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Fredholm operators and nonuniform exponential dichotomies

Chaos, Solitons & Fractals, 2016
We show that the existence of a nonuniform exponential dichotomy for a one-sided sequence $(A_m)_{; ; ; ; m\ge0}; ; ; ; $ of invertible $d\times d$ matrices is equivalent to the Fredholm property of a certain linear operator between spaces of bounded sequences.
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
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Notes on generalized exponential dichotomies

Acta Mathematicae Applicatae Sinica, 1996
Consider the linear differential system \[ dx/dt= A(t)x\tag{\(*\)} \] with \(x\in\mathbb{R}^n\) and \(A\in C(J, L(\mathbb{R}^n, \mathbb{R}^n))\) where \(J\) is some interval in \(\mathbb{R}\). Let \(X(t)\) be the fundamental matrix of \((*)\) satisfying \(X(0)= I\). \((*)\) is said to have a generalized exponential dichotomy (GED) on \(J\) if there are
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Admissibility for exponential dichotomies in average

Stochastics and Dynamics, 2015
We characterize completely the notion of an exponential dichotomy in average in terms of an admissibility property. The notion corresponds to a generalization of that of an exponential dichotomy to measurable cocycles acting on L1 functions with respect to a given probability measure. The admissibility property is described in terms of the injectivity
Barreira, Luis, Dragičević, Davor, Valls, Claudia   +2 more
openaire   +3 more sources