Nullity bounds for certain Hamiltonian delay equations. (English) Zbl 1514.37085

Frauenfelder, Urs

Kyoto J. Math. 63, No. 1, 195-209 (2023).

Author’s 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.

Reviewer: Abderrazek Benhassine (Monastir)

MSC:

37J51	Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods
37J46	Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems
37J06	General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants
34K17	Transformation and reduction of functional-differential equations and systems, normal forms

Keywords:

nullity bounds; Hamiltonian; delay equations

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