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Expansivity for optical Hamiltonian systems with two degrees of freedom. (English. Abridged French version) Zbl 0790.58030

The authors’ abstract: “Let \(H\) be an optical Hamiltonian on \(T^*M\), where \(M\) is a compact oriented surface. Let \(h\) be the maximum of \(H\) over the zero section of \(T^*M\). We show that if the Hamiltonian flow of \(H\) is expansive on the compact regular energy level \(H^{- 1}(\sigma)\), then there are no conjugate points provided \(\sigma > h\). We also show that if \(H\) is symmetric and \(\sigma < h\), then the Hamiltonian flow of \(H\) on \(H^{-1} (\sigma)\) cannot be expansive.”.
Reviewer: L.Stoyanov (Perth)

MSC:

37D99 Dynamical systems with hyperbolic behavior
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