4 papers
A Morse-Family Integrator for Hamilton--Jacobi Dynamics Across Caustics
F. Jiménez Alburquerque, M. Leok, C. Sardón +1
We develop a geometric framework for implicit discrete Hamiltonian systems based on discrete Morse families, Lagrangian relations, and discrete analogues of Tulczyjew's triple. The…
Exact integration of Hamiltonian dynamics via Jacobi and Poisson Cinf-structures
A. J. Pan-Collantes, C. Sardón, X. Zhao
We develop a geometric framework for the exact integration of Hamiltonian systems based on triangular closure relations among a finite family of functions. Unlike Liouville-Arnold…
Symmetries and Weighted Integrability of Vector Fields with Jacobi Multipliers
C. Sardón, X. Zhao
In this paper, we investigate analytic divergence-free vector fields and vector fields admitting a Jacobi multiplier on -dimensional Riemannian manifolds. We first introduce a f…
(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
C. Sardón, X. Zhao
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the…