Variational principle for contact Tonelli Hamiltonian systems

Abstract

We establish an implicit variational principle for the equations of the contact flow generated by the Hamiltonian $H(x,u,p)$ with respect to the contact 1-form $\hat{I}\pm =du-pdx$ under Tonelli and Osgood growth assumptions. It is the first step to generalize Mather's global variational method from the Hamiltonian dynamics to the contact Hamiltonian dynamics.

arXiv admin note: text overlap with arXiv:1408.3791