Title: Exact relations between homoclinic and periodic orbit actions in chaotic systems,
Abstract: Homoclinic and unstable periodic orbits in chaotic systems play central roles
in various semiclassical sum rules. The interferences between terms are
governed by the action functions and Maslov indices. In this article, we
identify geometric relations between homoclinic and unstable periodic orbits,
and derive exact formulae expressing the periodic orbit classical actions in
terms of corresponding homoclinic orbit actions plus certain phase space areas.
The exact relations provide a basis for approximations of the periodic orbit
actions as action differences between homoclinic orbits with well-estimated
errors. This make possible the explicit study of relations between periodic
orbits, which results in an analytic expression for the action differences
between long periodic orbits and their shadowing decomposed orbits in the cycle
expansion.