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Zbl 0935.34044
Hong, Jialin; Obaya, R.; Gil, A.S.
Exponential trichotomy and a class of ergodic solutions of differential equations with ergodic perturbations. (English)
[J] Appl. Math. Lett. 12, No.1, 7-13 (1999). ISSN 0893-9659

The existence of a class of ergodic solutions to some differential equations is investigated by using exponential trichotomy. An application to the Hill equation with an ergodic forcing function is given. \par One of the two main theorems is that if $\dot{x} = A(t)x$ admits an exponential trichotomy then $\dot{x} = A(t)x + f(t)$ has at least one ergodic solution for every ergodic $f$, with a special class of ergodic functions. The second theorem allows $f$ to depend on $x$ with a sufficiently small Lipschitz constant.
[S.Siegmund (Augsburg)]

MSC 2000:: *34D09 Dichotomy, trichotomy
34D10 Stability perturbations of ODE
34F05 ODE with randomness

Keywords: ergodic solutions; exponential trichotomy; stability; Hill equation; differential equations

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