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A survey of the recent results on characterizations of exponential stability and dichotomy over finite dimensional spaces. (English) Zbl 07238388
Summary: The main purpose of this article is the investigation of the recent advances on the exponential stability and dichotomy of autonomous and nonautonomous linear differential systems, in both continuous and discrete cases i.e. $$\dot x(t)=Ax(t)$$, $$\dot x(t)=A(t)x(t)$$, $$x_{n+1}=Ax_n$$ and $$x_{n+1}=A_nx_n$$ in terms of the boundedness of solutions of some Cauchy problems, where $$A$$, $$A_n$$, and $$A(t)$$ are square matrices, for any $$n\in\mathbb{Z}_+$$ and $$t\in\mathbb{R}_+$$.
##### MSC:
 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34D09 Dichotomy, trichotomy of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 37C60 Nonautonomous smooth dynamical systems 39A12 Discrete version of topics in analysis 34A30 Linear ordinary differential equations and systems, general
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