Floer homology for non-resonant magnetic fields on flat tori

2013/05/14 by Urs Frauenfelder, Frauenfelder, Urs, Will J. Merry +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.1305.3141

20 pages, V2 - fixed problem with fonts not displaying properly

arxiv created 2013/05/15 · arxiv updated 2013/05/16

Abstract

In this article we define and compute the Novikov Floer homology associated to a non-resonant magnetic field and a mechanical Hamiltonian on a flat torus T^2N. As a result, we deduce that this Hamiltonian system always has 2N+1 contractible solutions, and generically even 2^2N contractible solutions. Moreover if there exists a non-degenerate non-contractible solution then there necessarily exists another.

Related

• Floer homology for magnetic fields with at most linear growth on the universal cover
• Monopoles and Landau-Ginzburg Models II: Floer Homology
• Floer homology for Hamiltonian PDEs: Fredholm theory
• Global realisation of magnetic fields as 1(1)/(2)D Hamiltonian systems
• Reidemeister torsion in Floer-Novikov theory and counting pseudo-holomorphic tori, I