arXiv subjects

María Eugenia García

Publications and source records attributed to María Eugenia García.

2 recordsLinked to original sources

arXiv2025

Homogeneous bi-Hamiltonian structures and integrable contact systems

Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator relating both Poisson structures. We show that the recursion operator relating two compatible Jacobi structures cannot produce a maximal set of functions in involution. However, as we illustrate with an example, bi-Hamiltonian structures can still be used to obtain a maximal set of functions in involution on a contact manifold, at the cost of symplectisation.

math-ph↗

arXiv2024

The Optimal Reduction of a 2-Body Problem in R^3

In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit expressions in order to deal with geometric and dynamical aspects of the reduction process. For this system, the standard assumptions of the Marsden-Weinstein reduction process are only partially satisfied while optimal reduction can be readily applied, and we study a comparison between those two reduction processes. We describe potential applications to the study of Post-Newtonian Hamiltonian systems for binary systems in astronomy.

math-ph↗