Symplectically degenerate maxima via generating functions

TL;DR

This paper offers a straightforward proof that symplectically degenerate maxima in Hamiltonian diffeomorphisms on a 2D torus are either non-isolated periodic points or have non-isolated average-action spectrum points, using generating functions.

Contribution

It provides a simple, generating function-based proof of a theorem by Nancy Hingston regarding symplectically degenerate maxima.

Findings

Symplectically degenerate maxima are non-isolated or have non-isolated average-action spectrum.

The proof simplifies understanding of the structure of periodic points in Hamiltonian dynamics.

The approach connects generating functions with properties of symplectically degenerate maxima.

Abstract

We provide a simple proof of a theorem due to Nancy Hingston, asserting that symplectically degenerate maxima of any Hamiltonian diffeomorphism of the standard symplectic 2d-torus are non-isolated contractible periodic points or their action is a non-isolated point of the average-action spectrum. Our argument is based on generating functions.