On the number of periodic classical trajectories in a Hamiltonian dynamical system

TL;DR

This paper develops path integral methods to analyze the number of periodic classical trajectories in general Hamiltonian systems, providing a lower bound for their count.

Contribution

It introduces a novel path integral approach to estimate the minimum number of periodic trajectories in arbitrary Hamiltonian systems.

Findings

Derived a lower bound for the number of periodic trajectories.

Extended analysis to non-energy conserving Hamiltonian systems.

Provided a new mathematical framework for classical trajectory enumeration.

Abstract

Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian system. In particular, we present a simple derivation of a lower bound for the number of periodic classical trajectories.