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 Tr. Mat. Inst. Steklova, 2007, Volume 256, Pages 31–53 (Mi tm454)

The Curvature and Hyperbolicity of Hamiltonian Systems

A. A. Agrachevab

a Steklov Mathematical Institute, Russian Academy of Sciences
b International School for Advanced Studies (SISSA)

Abstract: Curvature-type invariants of Hamiltonian systems generalize sectional curvatures of Riemannian manifolds: the negativity of the curvature is an indicator of the hyperbolic behavior of the Hamiltonian flow. In this paper, we give a self-contained description of the related constructions and facts; they lead to a natural extension of the classical results about Riemannian geodesic flows and indicate some new phenomena.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 256, 26–46

Bibliographic databases:

Document Type: Article
UDC: 519.6

Citation: A. A. Agrachev, “The Curvature and Hyperbolicity of Hamiltonian Systems”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Tr. Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 31–53; Proc. Steklov Inst. Math., 256 (2007), 26–46

Citation in format AMSBIB
\Bibitem{Agr07} \by A.~A.~Agrachev \paper The Curvature and Hyperbolicity of Hamiltonian Systems \inbook Dynamical systems and optimization \bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov \serial Tr. Mat. Inst. Steklova \yr 2007 \vol 256 \pages 31--53 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm454} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336892} \zmath{https://zbmath.org/?q=an:1153.37346} \transl \jour Proc. Steklov Inst. Math. \yr 2007 \vol 256 \pages 26--46 \crossref{https://doi.org/10.1134/S0081543807010026} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248402457} 

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This publication is cited in the following articles:
1. A. A. Agrachev, “Well-posed infinite horizon variational problems on a compact manifold”, Proc. Steklov Inst. Math., 268 (2010), 17–31
2. Jakubczyk B., Krynski W., “Vector Fields with Distributions and Invariants of ODEs”, J. Geom. Mech., 5:1 (2013), 85–129
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