Abstract
We present some results about fixed points and periodic points for planar maps which are motivated by the analysis of the twist maps occurring in the Poincaré–Birkhoff fixed point theorem and in the study of geometric configurations associated to the linked twist maps arising in some problems of chaotic fluid mixing. Applications are given to the existence and multiplicity of periodic solutions for some planar Hamiltonian systems and, in particular, to the second-order nonlinear equation \(\ddot{x} + f(t,x) = 0\).
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The authors thank the referee for the careful checking of the manuscript and the pertinent remarks.
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Pascoletti, A., Zanolin, F. (2013). From the Poincaré–Birkhoff Fixed Point Theorem to Linked Twist Maps: Some Applications to Planar Hamiltonian Systems. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_14
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DOI: https://doi.org/10.1007/978-1-4614-7333-6_14
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