On weak exponential expansiveness of skew-evolution semiflows in Banach spaces

Yue, Tian; Song, Xiaoqiu; Li, Dongqing

doi:10.1186/1029-242x-2014-165

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…The connections between the dichotomy and splitting property were emphasized in [20]. The notion of skew-evolution semiflow was already adopted and its applicability emphasized by Bento and Silva (see [21]), Hai (see [22,23]), and Yue et al (see [24]).…”

Section: Introductionmentioning

confidence: 99%

A General Framework for Splitting Concepts for Cocycles over Generalized Nonautonomous Dynamical Systems

Stoica

2017

Mathematical Problems in Engineering

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While the classic theory of exponential dichotomy deals with differential and difference equations with uniquely determined forward and backward solutions, nowadays, applications in engineering require having corresponding theory for equations whose backward solutions are not guaranteed to exist or to be unique. To this goal, we will consider general dichotomic behaviors that consist in assuming the existence of splitting into invariant subspaces, where the norms of the evolution trajectories are bounded by some functions that depend on the initial and final times.

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Section: Introductionmentioning

confidence: 99%

A General Framework for Splitting Concepts for Cocycles over Generalized Nonautonomous Dynamical Systems

Stoica

2017

Mathematical Problems in Engineering

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“…The notion of skew-evolution semiflow considered in this paper and introduced by us in [23] generalizes the concepts of semigroups, evolution operators, and skewproduct semiflows and seems to be more appropriate for the study of the asymptotic behavior of the solutions of evolution equations in the nonuniform case, as they depend on three variables. The applicability of the notion has been studied in [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows

Stoica

2016

Discrete Dynamics in Nature and Society

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The aim of this paper is to highlight current developments and new trends in the stability theory. Due to the outstanding role played in the study of stable, instable, and, respectively, central manifolds, the properties of exponential dichotomy and trichotomy for evolution equations represent two domains of the stability theory with an impressive development. Hence, we intend to construct a framework for an asymptotic approach of these properties for discrete dynamical systems using the associated skew-evolution semiflows. To this aim, we give definitions and characterizations for the properties of exponential stability and instability, and we extend these techniques to obtain a unified study of the properties of exponential dichotomy and trichotomy. The results are underlined by several examples.

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On dichotomy and splitting issues for evolution equations

Stoica

2018

AIP Conference Proceedings

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On weak exponential expansiveness of skew-evolution semiflows in Banach spaces

Cited by 8 publications

References 16 publications

A General Framework for Splitting Concepts for Cocycles over Generalized Nonautonomous Dynamical Systems

A General Framework for Splitting Concepts for Cocycles over Generalized Nonautonomous Dynamical Systems

Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows

On dichotomy and splitting issues for evolution equations

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