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arXiv · 1911.05962

The globalization problem of the Hamilton-DeDonder-Weyl equations on a local $k$-symplectic framework

Oğul Esen·Manuel de León·Cristina Sardón·Marcin Zajac
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Abstract

In this paper we aim at addressing the globalization problem of Hamilton-DeDonder-Weyl equations on a local $k$-symplectic framework and we introduce the notion of {\it locally conformal $k$-symplectic (l.c.k-s.) manifolds}. This formalism describes the dynamical properties of physical systems that locally behave like multi-Hamiltonian systems. Here, we describe the local Hamiltonian properties of such systems, but we also provide a global outlook by introducing the global Lee one-form approach. In particular, the dynamics will be depicted with the aid of the Hamilton--Jacobi equation, which is specifically proposed in a l.c.k-s manifold.

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Oğul Esen, Manuel de León, Cristina Sardón, Marcin Zajac. 2019-11-14. The globalization problem of the Hamilton-DeDonder-Weyl equations on a local $k$-symplectic framework. https://arxiv.org/abs/1911.05962

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