Multiple periodic solutions and complex dynamics for second order ODEs via linked twist maps
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" e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=336 |
| Summary: | 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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| ISSN: | 1417-3875 1417-3875 |