On geometric detection of periodic solutions and chaotic dynamics

R. Srzednicki, Jagiellonian University, Krakow, Poland

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 27. (2000), pp. 1-11.

Abstract: In this note we sketch some results concerning a geometric method for periodic solutions of non-autonomous time-periodic differential equations. We give the definition of isolating chain and we provide a theorem on the existence of periodic solutions inside isolating chains. We recall some results on existence of chaotic dynamics which can be proved by the theorem. We provide several examples of equations in which the presented theorems can be applied.

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