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A topological approach to the problem of chaotic tides |
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| Institution: | 1. Dipartimento di Matematica Pura ed Applicata, Univ. di Modena e Reggio Emilia, Via Campi, 213b, 41100 Modena, Italy;2. Faculdade de Ciências da Universidade de Lisboa. CMAF-CIO, Campo Grande 1749-016 Lisboa, Portugal;1. Instituto Interdisciplinar de Matemáticas, Universidad Complutense de Madrid, Madrid, Spain;2. Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Trieste, Italy |
| Abstract: | We study the existence of subharmonic solutions and solutions with complicated dynamics in a Duffing-type equation which arises from the study of forced tides. This is a model which involves an almost enclosed basin, connected to the sea by a narrow strait. Such a basin turns out to be a nonlinear Helmholtz resonator. The proofs are based on developments of the theory of topological horseshoes in connection with some geometric features associated to linked twist maps. |
| Keywords: | Nonautonomous Duffing equations Poincaré map Subharmonic solutions Topological horseshoes Chaotic dynamics Tides |
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