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Abstract: This paper studies the existence of invariant smooth Lagrangian graphs forTonelli Hamiltonian systems with symmetries. In particular, we consider TonelliHamiltonians with n independent but not necessarily involutive constants ofmotion and obtain two theorems reminiscent of the Liouville-Arnold theorem.Moreover, we also obtain results on the structure of the configuration spacesof such systems that are reminiscent of results on the configuration space ofcompletely integrable Tonelli Hamiltonians.



Author: Leo T. Butler, Alfonso Sorrentino

Source: https://arxiv.org/



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