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Ergodic type solutions of some differential equations. (English) Zbl 0995.34048
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).
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. For the entire collection see [Zbl 0961.00018].

34F05ODE with randomness
34C27Almost and pseudo-almost periodic solutions of ODE
34C11Qualitative theory of solutions of ODE: growth, boundedness