An asymptotic relationship between homoclinic points and periodic orbit stability exponents

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.

arXiv comment6 pages, 3 figures. arXiv admin note: text overlap with arXiv:1712.05568

References in corpus (5)

• Geometry and Topology of Escape I: Epistrophes
• Analytical description of the structure of chaos
• Exact relations between homoclinic and periodic orbit actions in chaotic systems
• Action differences between fixed points and accurate heteroclinic orbits
• Geometric determination of heteroclinic and unstable periodic orbit classical actions