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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 fL(, d ) is said to be ergodic if the limit

lim T 1 2T -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.

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