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On Exponential Dichotomy of Variational Difference Equations [PDF]
Discrete Dynamics in Nature and Society, 2009 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.
Bogdan Sasu
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Roughness of (ℤ+,ℤ-)-Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces [PDF]
The Scientific World Journal, 2014 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.
Nicolae Lupa
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On the Exponents of Exponential Dichotomies [PDF]
Mathematics, 2020 An exponential dichotomy is studied for linear differential equations. A constructive method is presented to derive a roughness result for perturbations giving exponents of the dichotomy as well as an estimate of the norm of the difference between the ...
Flaviano Battelli, Michal Fečkan
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On Some Characterizations for Uniform Dichotomy of Evolution Operators in Banach Spaces
Mathematics, 2022 The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces.
Rovana Boruga (Toma), Mihail Megan
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Nonuniform Dichotomy with Growth Rates of Skew-Evolution Cocycles in Banach Spaces
Axioms, 2023 This paper presents integral charaterizations for nonuniform dichotomy with growth rates and their correspondents for the particular cases of nonuniform exponential dichotomy and nonuniform polynomial dichotomy of skew-evolution cocycles in Banach spaces.
Ariana Găină +2 more
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On uniform dichotomy in mean of stochastic skew-evolution semiflows in Banach spaces
Annals of the West University of Timisoara: Mathematics and Computer Science, 2023 In this paper we consider three concepts of uniform dichotomy in mean for stochastic skew-evolution semiflows: uniform exponential dichotomy in mean, uniform polynomial dichotomy in mean and uniform h- dichotomy in mean.
Fülöp Tímea Melinda Személy
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Exponential dichotomy for evolution families on the real line
Abstract and Applied Analysis, 2006 We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)).
Adina Luminiţa Sasu
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Weak topologies for Carathéodory differential equations: continuous dependence, exponential dichotomy and attractors [PDF]
, 2019 Producción CientíficaWe introduce new weak topologies and spaces of Carathéodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields. The induced local skew-product flow is proved
Longo, Iacopo Paolo +2 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2022 For a large class of nonautonomous linear delay equations with distributed delay, we obtain the equivalence of hyperbolicity, with the existence of an exponential dichotomy, and Ulam–Hyers stability.
Luis Barreira, Claudia Valls
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Exponential dichotomy for noninvertible linear difference equations [PDF]
Journal of Difference Equations and Applications, 2021 The final version of the paper will appear in the Journal of difference equations and ...
Battelli, F., Franca, M., Palmer, K. J.
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