Paternain, Gabriel P.; Paternain, Miguel Expansivity for optical Hamiltonian systems with two degrees of freedom. (English. Abridged French version) Zbl 0790.58030 C. R. Acad. Sci., Paris, Sér. I 316, No. 8, 837-841 (1993). 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) Cited in 2 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior Keywords:optical Hamiltonian system; expansive flow; conjugate points PDFBibTeX XMLCite \textit{G. P. Paternain} and \textit{M. Paternain}, C. R. Acad. Sci., Paris, Sér. I 316, No. 8, 837--841 (1993; Zbl 0790.58030)