Existence of closed characteristics on compact convex hypersurfaces in R 2 n

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Existence of closed characteristics on compact convex hypersurfaces in R 2 n

Wang, Wei

Calculus of variations and partial differential equations, 01/2016, Volume: 55, Issue: 1

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In this paper, we prove there exist at least n+12+1 geometrically distinct closed characteristics on every compact convex hypersurface Σ in R2n, where n≥2. In particular, this gives a new proof in the case n=3 to a long standing conjecture in Hamiltonian analysis. Moreover, there exist at least n2+1 geometrically distinct non-hyperbolic closed characteristics on Σ provided the number of geometrically distinct closed characteristics on Σ is finite.

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