Scaling of the diffusion coefficient on the normal form remainder in doubly resonant domains

TL;DR

This paper provides theoretical estimates on how the diffusion coefficient in 3-degree-of-freedom Hamiltonian systems depends on the size of the normal form remainder within doubly resonant domains.

Contribution

It introduces a theoretical framework linking the diffusion coefficient to the normal form remainder in doubly resonant regions of Hamiltonian systems.

Findings

Diffusion coefficient scales with the size of the normal form remainder.

Provides estimates for the dependence of diffusion on system parameters.

Enhances understanding of transport in resonant Hamiltonian systems.

Abstract

An outline of theoretical estimates is given regarding the dependence of the value of the diffusion coefficient $D$ on the size $R$ of the remainder of the normal form in doubly or simply resonant domains of the action space of 3dof Hamiltonian systems.