From the Poincaré-Birkhoff Fixed Point Theorem to Linked Twist Maps: Some Applications to Planar Hamiltonian Systems

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 ẍ+ f (t,x) = 0. © Springer Science+Business Media New York 2013.