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Hyperbolic characteristics on star-shaped hypersurfaces
Authors:Chun-gen Liu  Yiming Long  
Institution:Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
Abstract:In this paper, we study the stability of closed characteristics on a starshaped compact smooth hypersurface Σ in Image 2n. We show that the Maslov-type mean index of such a closed characteristic is independent of the choice of the Hamiltonian functions, and prove that on Σ either there are infinitely many closed characteristics, or there exists at least one nonhyperbolic closed characteristic, provided every closed characteristic possesses its Maslov-type mean index greater than 2 when n is odd, and greater than 1 when n is even.
Keywords:Hamiltonian systems  Maslov-type mean index  iterations  hyperbolic closed characteristics  star-shaped energy hypersurface
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