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Period two implies chaos for a class of ODEs |
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| Authors: | Franco Obersnel Pierpaolo Omari |
| Affiliation: | Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy ; Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy |
| Abstract: | We extend a result of J. Andres and K. Pastor concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase T. Y. Li and J. A. Yorke by loosely saying that in this setting even period two implies chaos. Similar results are obtained for a class of differential inclusions. |
| Keywords: | First order scalar ordinary differential equation periodic solution subharmonic solution lower and upper solutions differential inclusion |
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