The Hormander index of symmetric periodic orbits

TL;DR

This paper derives a formula for the Hormander index of symmetric periodic orbits and their iterates using Chebyshev polynomials, linking symplectic geometry and polynomial analysis.

Contribution

It introduces a novel formula for calculating the Hormander index of symmetric periodic orbits and their iterates in terms of Chebyshev polynomials.

Findings

Formula for Hormander index in terms of Chebyshev polynomials

Application to symmetric periodic orbits and their iterates

Enhanced understanding of Lagrangian intersection points

Abstract

A symmetric periodic orbit is a special kind of periodic orbit that can also be regarded as a Lagrangian intersection point. Therefore it has two Maslov indices whose difference is the Hormander index. In this paper we provide a formula for the Hormander index of a symmetric periodic orbit and its iterates in terms of Chebyshev polynomials.