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Zbl 0995.34048
Hong, Jialin; Obaya, Rafael
Ergodic type solutions of some differential equations. (English)
[A] Vajravelu, K. (ed.), Differential equations and nonlinear mechanics. Proceedings of the international conference, Orlando, FL, USA, March 17-19, 1999. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 528, 135-152 (2001). ISBN 0-7923-6867-3/hbk

A function $f \in L({\bbfR},{\bbfR}^d)$ is said to be ergodic if the limit $$ \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^T f(t) dt = M(f) $$ exists. E.g., almost-periodic functions are ergodic. The existence of ergodic solutions to differential equations is of practical importance. This summary contains results on the existence of ergodic solutions.
[Stefan Siegmund (Augsburg)]

MSC 2000:: *34F05 ODE with randomness
34C27 Almost periodic solutions of ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: almost-periodic solutions; ergodic solutions

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