Implicit contact dynamics and Hamilton-Jacobi theory

In this paper we propose a Hamilton-Jacobi theory for implicit contact Hamiltonian systems in two different ways. One is the understanding of implicit contact Hamiltonian dynamics as a Legendrian submanifold of the tangent contact space, and another is as a Lagrangian submanifold of a certain symplectic space embedded into the tangent contact space. In these two scenarios we propose a Hamilton-Jacobi theory specifically derived with the aid of Herglotz Lagrangian dynamics generated by non-regular Lagrangian functions. MSC2020 classification: 37J55; 53D10; 70H20.

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