Complex Dynamics in Pendulum-Type Equations with Variable Length |
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Authors: | Alessandro Margheri Carlota Rebelo Fabio Zanolin |
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Institution: | 1. Departamento de Matemática, Fac. Ciências de Lisboa, Campo Grande, Edifício C6, piso 2, 1749-016, Lisboa, Portugal 2. Department of Mathematics and Computer Science, University of Udine, via delle Scienze 206, 33100, Udine, Italy
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Abstract: | We prove the existence of complex dynamics for a generalized pendulum type equation with variable length. The solutions we find switch from an oscillatory behavior around the stable vertical position to a rotational type behavior crossing the unstable position with positive or negative velocity following any prescribed two-sided sequence of symbols. Moreover, to any periodic sequence of symbols corresponds a periodic solution of the equation. The proof is based on a topological approach and the results are robust with respect to small perturbations. In particular a small friction term can be added to the equation. |
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