An integer optimization problem for non-Hamiltonian periodic flows

2013/07/25 by Álvaro Pelayo, Pelayo, Álvaro, Silvia Sabatini +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Quantum chaos and dynamical systems #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1307.6766

Abstract

Let C be the class of compact 2n-dimensional symplectic manifolds M for which the first or (n-1) Chern class vanish. We point out an integer optimization problem to find a lower bound B(n) on the number of equilibrium points of non-Hamiltonian symplectic periodic flows on manifolds M in C. As a consequence, we confirm in dimensions 2n in 8,10,12,14,18,20, 22 a conjecture for unitary manifolds made by Kosniowski in 1979 for the subclass C.

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• Fixed points of symplectic periodic flows
• Leafwise fixed points for C⁰-small Hamiltonian flows
• Fermat and the number of fixed points of periodic flows
• Periodic Hamiltonian flows on four dimensional manifolds
• Periodic orbits of Hamiltonian flows near symplectic extrema