Titlebook: Almost Periodicity, Chaos, and Asymptotic Equivalence; Marat Akhmet Book 2020 Springer Nature Switzerland AG 2020 Chaos.Li-Yorke Chaos.Alm

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Introduction,ecewise-constant argument, and asymptotical equivalence. It consists of four parts. In the first one, the origins of the almost periodic functions and almost periodic solutions of differential equations are shortly presented. Next, the process of development of the theory of discontinuous almost per

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Generalities for Impulsive Systems,mprehension of the main body of the book. This is, first of all, a description of piecewise continuous functions and their points of discontinuity. Analysis instruments such as equivalent integral equations and the Gronwall-Bellman lemma for piecewise continuous functions are carefully described. St

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Discontinuous Almost Periodic Functions,ential equations with different types of discontinuity, but also unbounded number sequences which are common instruments to introduce and analyze discontinuities not only in impulsive systems, but also in differential equations with discontinuous right-hand side, differential equations with piecewis

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Discontinuous Almost Periodic Solutions,elopment of not only properties for the functions themselves, but also new conditions for the impulsive systems, which suppose to admit the solutions. If the theory of almost periodic functions has been developed in the last chapter, the present chapter considers conditions for linear and quasilinea

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Bohr and Bochner Discontinuities,he definition and it is obtained as the theorem. Nevertheless, the property of conditional uniform continuity is assumed in the definition of the discontinuous almost periodic function. Thus, if one wants to follow the classical way of the theory construction, a new approach has to be found. Initial

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Exponentially Dichotomous Linear Systems of Differential Equations with Piecewise Constant Argumentern, first of all, linear systems of differential equations are under discussion. An exceptional attention to the exponential dichotomy is given at the first time in literature in the paper Akhmet (Discontinuity Nonlinearity Complexity 1:337-352, 2012). This time we present integral representation f

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Ancestor

Differential Equations on Time Scales Through Impulsive Differential Equations,ive differential equations (IDE). DETC are in some sense more general than dynamic equations on time scales. Basic properties of linear systems, existence and stability of periodic solutions and almost periodic solutions are considered. Appropriate examples are given to illustrate the theory.

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