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)
Pascoletti, A., Pireddu, M., Zanolin, F. (2008). Multiple periodic solutions and complex dynamics for second order ODEs via linked twist maps. Intervento presentato a: 8th Coll. Qualitative Theory of Diff. Equ., Szeged.
Multiple periodic solutions and complex dynamics for second order ODEs via linked twist maps
PIREDDU, MARINA;
2008
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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