Second order Lagrangian twist systems: simple closed characteristics (Q2781366)

The authors investigate Lagrangian systems whose Lagrangian depends on the second derivatives and so the Euler-Lagrange equation is of the fourth order. The Hamiltonian systems, coming from second order Lagrangian ones, have a certain global section where in many situations the return map is quite analogous to a monotone area-preserving twist map. The systems with such property are called by the authors twist systems. The paper is devoted to basic properties of twist systems and to the study of their simple closed characteristics, the periodic trajectories that, when represented in the configuration space of Lagrangian system (i.e. with only states and first derivatives taken into account), are simple closed curves.