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)
paper
Nonlinear second order ODEs, periodic solutions, chaotic dynamics, linked twist mappings
English
8th Coll. Qualitative Theory of Diff. Equ.
2007
2008
14
1
32
http://www.math.u-szeged.hu/ejqtde/p336.pdf
none
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/46082
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