Coexistence of random subharmonic oscillations
by
Jan Andres
Palacky University in Olomouc, Czech Republic

Improving our earlier results [AP], F. Obersnel and P. Omari [OO] (cf. [AFP]) obtained an interesting theorem saying that "if, for a fixed k>1, a time-periodic scalar ODE possesses a subharmonic solution of order k then, for every positive integer n, it also admits a subharmonic solution of order n". In our talk, we shall extend their theorem, by means of a proposition [An] allowing us to deal with periodic orbits in a deterministic way, to random differential equations and inclusions.

References

[An] J. Andres: Randomization of Sharkovskii-type theorems. Submitted.

[AFP] J. Andres, T. Fürst and K. Pastor: Period two implies all periods for a class of ODEs: a multivalued map approach. Proc. Amer. Math. Soc., to appear.

[AP] J. Andres and K. Pastor: A version of Sharkovskii's theorem for differential equations. Proc. Amer. Math. Soc. 133 (2005), 449-453.

[OO] F. Obersnel and P. Omari: Period two impies chaos for a class of ODEs. Proc. Amer. Math. Soc. 135 (2007), 2055-2058.

Date received: April 24, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caum-18.