Two short closed geodesics on a sphere of odd dimension

Abstract

We show that for an open and dense set non-reversible Finsler metrics on a sphere of odd dimension $n=2m-1\ge 3$ there is a second closed geodesic with Morse index $\le 4(m+2)(m-1)+2.$

16 pages, revised version, to appear in "Calc.Var.Partial Diff. Equ."