Almost Existence From the Feral Perspective and Some Questions

TL;DR

This paper investigates the 'almost existence' phenomenon for periodic orbits in Hamiltonian systems, using feral curves and adiabatic degeneration to establish results in both known and new cases.

Contribution

It introduces novel methods involving feral curves and adiabatic degeneration to analyze the existence of periodic orbits in Hamiltonian dynamics.

Findings

Established 'almost existence' results in new cases

Applied feral curves to Hamiltonian systems

Utilized adiabatic degeneration techniques

Abstract

This paper is concerned with the "almost existence" phenomenon for periodic orbits of Hamiltonian dynamical systems. In particular, we recover this result in both some standard and some novel cases via feral curves and an adiabatic degeneration.