Monotone twist maps and periodic solutions of systems of Duffing type (Q2927885)

Existence of multiple periodic solutions is studied for weakly coupled Duffing type systems: NEWLINE\[NEWLINE x_i''+x_i^3= \partial _iP(t,x_1,x_2), \qquad i=1,2. NEWLINE\]NEWLINENEWLINENEWLINEInstead of the variational approach the authors apply here a framework based on some generalization of the Poincaré-Birkhoff theorem to higher dimensions (comp. Section 2.8 in [\textit{J. Moser} and \textit{E. J. Zehnder}, Notes on dynamical systems. Courant Lecture Notes in Mathematics 12. Providence, RI: American Mathematical Society (AMS); New York, NY: Courant Institute of Mathematical Sciences (2005; Zbl 1087.37001)]). This method of proof gives a precise information on the oscillatory properties of these solutions.