We study periodic orbits of the Reeb vector field on a nondegenerate dynamically convex starshaped hypersurface in R-2n along the lines of Long and Zhu 24, but using properties of the S-1 - equivariant symplectic homology. We prove that there exist at least n distinct simple periodic orbits on any nondegenerate starshaped hypersurface in R-2n satisfying the condition that the minimal Conley Zehnder index is at least n - 1. The condition is weaker than dynamical convexity.
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