Using Lagrangian descriptors to calculate the Maslov index of periodic orbits

TL;DR

This paper introduces a simple method using Lagrangian descriptors to compute the Maslov index of periodic orbits in two-degree-of-freedom systems, simplifying the process for semiclassical quantization.

Contribution

The paper presents a novel, straightforward technique for calculating the Maslov index using Lagrangian descriptors, applicable to two-dimensional systems.

Findings

Method successfully applied to the two-dimensional coupled quartic oscillator.

Provides a less complex alternative to existing rigorous techniques.

Facilitates semiclassical quantization in non-integrable systems.

Abstract

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of non-integrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.