Seifert conjecture in the even convex case

CDSNS Colloquium
Monday, March 30, 2015 - 11:00am
1 hour (actually 50 minutes)
Slikes 005
Nankai University, China
The iteration theory for Lagrangian Maslov index is a very useful tool    in studying the multiplicity of brake orbits of Hamiltonian systems.  In  this talk, we show how to use this theory to prove that there exist at    least $n$ geometrically distinct brake orbits on every $C^2$ compact convex symmetric hypersurface in $\R^{2n}$ satisfying the reversible condition. As a consequence, we show that if    the Hamiltonian function is convex and even, then Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integer $n$.