2023/03/08 by Robert I. McLachlan, McLachlan, Robert I, David McLaren +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2303.04300
openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of this paper is the discretization of Hamiltonian systems of the form x = -K ∇ W(x), where K is a constant symmetric matrix and W\colonℝn→ ℝ is a polynomial of degree d≤ 4 in any number of variables n. The discretization uses the method of polarization and preserves both the energy and the invariant measure of the differential equation, as well as the dimension of the phase space. This generalises earlier work for discretizations of first order systems with d=3, and of second order systems with d=4 and n=1.