An asymptotic relationship between homoclinic points and periodic orbit stability exponents

TL;DR

This paper establishes an asymptotic relationship linking the stability exponents of periodic orbits to the phase-space positions of specific homoclinic points, enhancing understanding of semiclassical trace formulas.

Contribution

It introduces a novel asymptotic relationship connecting orbit stability exponents with homoclinic point positions in phase space.

Findings

Stability exponents are asymptotically related to homoclinic points.

The relationship simplifies the analysis of semiclassical trace formulas.

Provides new insights into the structure of phase space.

Abstract

The magnitudes of the terms in periodic orbit semiclassical trace formulas are determined by the orbits' stability exponents. In this paper, we demonstrate a simple asymptotic relationship between those stability exponents and the phase-space positions of particular homoclinic points.