Multiple periodic solutions for one-sided sublinear systems: A refinement of the Poincaré-Birkhoff approach

2019/01/27 by Dondè, Tobia, Zanolin, Fabio
#34C25 #34C28 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.09406

Abstract

In this paper we prove the existence of multiple periodic solutions (harmonic and subharmonic) for a class of planar Hamiltonian systems which include the case of the second order scalar ODE x'' + a(t)g(x) = 0 with g satisfying a one-sided condition of sublinear type. We consider the classical approach based on the Poincaré-Birkhoff fixed point theorem as well as some refinements on the side of the theory of bend-twist maps and topological horseshoes. The case of complex dynamics is investigated, too.

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