Multiple periodic solutions and complex dynamics for second order ODEs via linked twist maps

A. Pascoletti, University of Udine, Italy
M. Pireddu, University of Udine, Italy
F. Zanolin, University of Udine, Italy

E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 14. (2008), pp. 1-32.

Abstract: We consider some nonlinear second order scalar ODEs of the form $x'' + f(t,x) =0,$ where $f$ is periodic in the $t$--variable and show the existence of infinitely many periodic solutions as well as the presence of complex dynamics, even in the case of certain apparently simple'' equations. We employ a topological approach based on the study of linked twist maps (and suitable modifications of their geometry).

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