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- W2963485498 abstract "Let (M n , g) denote a closed Riemannian manifold (n ≥ 3) which admits a metric of negative curvature (not necessarily equal to g). Let ω 1 := ω 0 + π*σ denote a twisted symplectic form on TM, where σ ∈ Ω 2 (M) is a closed 2-form and ω 0 is the symplectic structure on TM obtained by pulling back the canonical symplectic form dx ∧ dp on T*M via the Riemannian metric. Let Σ k be the hypersurface [Formula: see text]. We prove that if n is odd and the Hamiltonian structure (Σ k , ω 1 ) is Anosov with C 1 weak bundles, then (Σ k , ω 1 ) is stable if and only if it is contact. If n is even and in addition the Hamiltonian structure is 1/2-pinched, then the same conclusion holds. As a corollary, we deduce that if g is negatively curved, strictly 1/4-pinched and σ is not exact then the Hamiltonian structure (Σ k , ω 1 ) is never stable for all sufficiently large k." @default.
- W2963485498 created "2019-07-30" @default.
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- W2963485498 date "2010-12-01" @default.
- W2963485498 modified "2023-09-27" @default.
- W2963485498 title "STABILITY OF ANOSOV HAMILTONIAN STRUCTURES" @default.
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- W2963485498 doi "https://doi.org/10.1142/s1793525310000434" @default.
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