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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 $f\in L\left(ℝ,{ℝ}^{d}\right)$ is said to be ergodic if the limit

$\underset{T\to \infty }{lim}\frac{1}{2T}{\int }_{-T}^{T}f\left(t\right)dt=M\left(f\right)$

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.

##### MSC:
 34F05 ODE with randomness 34C27 Almost and pseudo-almost periodic solutions of ODE 34C11 Qualitative theory of solutions of ODE: growth, boundedness
##### Keywords:
almost-periodic solutions; ergodic solutions