Preserving Problem of Local Boundedness of Hamiltonian Dynamical Systems by Symplectic Discretization

TL;DR

This paper investigates how symplectic discretization methods can maintain the local boundedness property of 2D Hamiltonian dynamical systems, ensuring numerical stability and fidelity to the continuous system.

Contribution

It provides conditions under which symplectic discretization preserves local boundedness in 2D Hamiltonian systems, a novel focus in numerical analysis.

Findings

Derived conditions for boundedness preservation

Enhanced understanding of symplectic discretization effects

Potential for improved numerical stability in simulations

Abstract

We have researched the condition for symplectic discretization to preserve local boundedness for the space of 2-dimensional Hamiltonian dynamical systems in this paper.