Nullity bounds for certain Hamiltonian delay equations

TL;DR

This paper introduces a class of Hamiltonian delay equations derived from an action functional and establishes uniform bounds on the kernel dimension of the Hessian at critical points.

Contribution

It provides the first analysis of nullity bounds for Hamiltonian delay equations related to orbit interactions.

Findings

Kernel of the Hessian has a uniformly bounded dimension at critical points

Introduces a new class of Hamiltonian delay equations from an action functional

Establishes nullity bounds for these equations

Abstract

In this paper we introduce a class of Hamilton delay equations which arise as critical points of an action functional motivated by orbit interactions. We show that the kernel of the Hessian at each critical point of the action functional satisfies a uniform bound on its dimension.