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A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in $\mathbf{R}^{2n}$
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classification
math.SGmath.DS
keywords
characteristicsclosedcompactdistinctexistgeometricallymathbfstar-shaped
abstract
In this paper, we prove that if all closed characteristics on a compact non-degenerate star-shaped hypersurface $\Sigma$ in $\mathbf{R}^{2n}$ are elliptic, then either there exist exactly $n$ geometrically distinct closed characteristics, or there exist infinitely many geometrically distinct closed characteristics.
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