Construction of symplectic systems from parameter-drift Hamiltonian maps

TL;DR

This paper demonstrates how parameter-drift maps can be embedded into extended phase space to form symplectic systems, enabling better analysis of their dynamics and transport phenomena.

Contribution

It introduces a novel embedding method that constructs autonomous symplectic maps from parameter-drift Hamiltonian maps, preserving key dynamics.

Findings

The symplectic map accurately reproduces the original system's dynamics.

Finite time Lyapunov exponents reveal limitations of ensemble diagnostics.

The approach offers new insights into transport in nonautonomous systems.

Abstract

We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase space that preserves key dynamics of the original system. Computing finite time Lyapunov exponents, the symplectic map shows limitations of ensemble-based diagnostics, common in the parameter-drift literature, and provides new insights into transport phenomena in these nonautonomous systems.