Degenerate Maxima in Hamiltonian Systems

2009/12/31 by Mike Chance, Chance, Mike
Mathematics · #53D05 (Primary) #65P10 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D05 #msc:65P10

paper · pdf · doi:10.48550/arxiv.1001.0184

13 pages

arxiv created 2009/12/31 · openalex publication_date 2009/12/31 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we explore loops of non-autonomous Hamiltonian diffeomorphisms with degenerate fixed maxima. We show that such loops can not have totally degenerate fixed global maxima. This has applications for the Hofer geometry of the group of Hamiltonians for certain symplectic 4 manifolds and also gives criteria for certain 4 manifolds to be uniruled.

Related

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• Degeneracy Index and Poincaré-Hopf Theorem
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