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 α=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.
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