Period two implies chaos for a class of ODEs
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- by Franco Obersnel and Pierpaolo Omari PDF
- Proc. Amer. Math. Soc. 135 (2007), 2055-2058 Request permission
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.References
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Additional Information
- Franco Obersnel
- Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy
- Email: obersnel@units.it
- Pierpaolo Omari
- Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy
- Email: omari@units.it
- Received by editor(s): February 1, 2006
- Received by editor(s) in revised form: February 28, 2006
- Published electronically: January 9, 2007
- Additional Notes: The first author acknowledges the support of G.N.A.M.P.A., in the setting of the project “Soluzioni periodiche di equazioni differenziali ordinarie”.
The second author acknowledges the support of M.I.U.R, in the setting of the P.R.I.N. project “Equazioni differenziali ordinarie e applicazioni”. - Communicated by: Carmen C. Chicone
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2055-2058
- MSC (2000): Primary 34C25, 34A60
- DOI: https://doi.org/10.1090/S0002-9939-07-08700-X
- MathSciNet review: 2299480