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• W3099756802 abstract "In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (`slicing vector fields') on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion." @default.
• W3099756802 created "2020-11-23" @default.
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• W3099756802 date "2016-01-26" @default.
• W3099756802 modified "2023-09-30" @default.
• W3099756802 title "Structural aspects of Hamilton–Jacobi theory" @default.
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• W3099756802 doi "https://doi.org/10.1142/s0219887816500171" @default.
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