3 papers
math-ph2026
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…
math-ph2025
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…
math-ph2025
(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…