1999/05/03 by John B. Etnyre, Etnyre, John B., Robert W. Ghrist +1
Mathematics · #57M25 #58F22 (secondary) #76C05(primary) 58F07 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT #msc:57M25 #msc:58F07 #msc:58F22
paper · pdf · doi:10.48550/arxiv.math/9905009
arxiv created 1999/05/03 · arxiv updated 2009/11/30
We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result on the Euler equations follows from this when combined with some contact-topological perspectives and a recent result of Hofer, Wyzsocki, and Zehnder.