1. Implicit contact dynamics and Hamilton-Jacobi theory.
- Author
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Esen, Oğul, Lainz Valcázar, Manuel, de León, Manuel, and Sardón, Cristina
- Subjects
- *
SYMPLECTIC spaces , *HAMILTON-Jacobi equations , *GEOMETRY - Abstract
In this paper, we introduce implicit Hamiltonian dynamics in the framework of contact geometry in two different ways: first, we introduce classical implicit Hamiltonian dynamics on a contact manifold, followed by evolution Hamiltonian dynamics. In the first case, implicit contact Hamiltonian dynamics is defined as a Legendrian submanifold of a tangent contact space, whilst the implicit evolution dynamic is understood as a Lagrangian submanifold of a certain symplectic space embedded into the tangent contact space. To conclude, we propose a geometric Hamilton-Jacobi theory for both of these formulations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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