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Tr. Mat. Inst. Steklova, 2000, Volume 231, Pages 46–63 (Mi tm511)  

This article is cited in 17 scientific papers (total in 17 papers)

Integrable Geodesic Flows on the Suspensions of Toric Automorphisms

A. V. Bolsinova, I. A. Taimanovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Integrable geodesic flows are studied on suspensions of toric automorphisms. It is shown that, for linear automorphisms with real spectrum, such flows always exist. Their entropy characteristics are investigated. In particular, in the case of hyperbolic automorphisms, we describe explicitly a closed invariant subset on which the topological entropy of the geodesic flow is positive.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 231, 42–58

Bibliographic databases:

UDC: 517.938.5
Received in December 1999

Citation: A. V. Bolsinov, I. A. Taimanov, “Integrable Geodesic Flows on the Suspensions of Toric Automorphisms”, Dynamical systems, automata, and infinite groups, Collected papers, Tr. Mat. Inst. Steklova, 231, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 46–63; Proc. Steklov Inst. Math., 231 (2000), 42–58

Citation in format AMSBIB
\Bibitem{BolTai00}
\by A.~V.~Bolsinov, I.~A.~Taimanov
\paper Integrable Geodesic Flows on the Suspensions of Toric Automorphisms
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 46--63
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm511}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1841751}
\zmath{https://zbmath.org/?q=an:1005.53064}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 42--58


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Jovanovic B., “On the integrability of geodesic flows of submersion metrics”, Letters in Mathematical Physics, 61:1 (2002), 29–39  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Bolsinov A.V., Jovanovic B., “Noncommutative integrability, moment map and geodesic flows”, Annals of Global Analysis and Geometry, 23:4 (2003), 305–322  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Bolsinov A.V., Jovanovic B., “Complete involutive algebras of functions on cotangent bundles of homogeneous spaces”, Mathematische Zeitschrift, 246:1–2 (2004), 213–236  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Bolsinov A.V., “Integrable geodesic flows on Riemannian manifolds: Construction and obstructions”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 57–103  crossref  mathscinet  zmath  isi
    5. Butler L.T., “Invariant fibrations of geodesic flows”, Topology, 44:4 (2005), 769–789  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. K. M. Zuev, “Spectrum of the Laplace–Beltrami operator on suspensions of toric automorphisms”, Sb. Math., 197:9 (2006), 1297–1308  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Kruglikov B.S., Matveev V.S., “Strictly non–proportional geodesically equivalent metrics have h(top)(g)=0”, Ergodic Theory and Dynamical Systems, 26:1 (2006), 247–266  crossref  mathscinet  zmath  isi  scopus  scopus
    8. A. A. Yakovlev, “Adiabatic Limits on Riemannian $\mathrm{Sol}$-Manifolds”, Math. Notes, 84:2 (2008), 297–299  mathnet  crossref  crossref  mathscinet  isi
    9. Calogero F., Leyvraz F., “How to embed an arbitrary Hamiltonian dynamics in a superintegrable (or just integrable) Hamiltonian dynamics”, Journal of Physics A–Mathematical and Theoretical, 42:14 (2009), 145202  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. A. A. Yakovlev, “Asymptotics of the spectrum of the Laplace operator on Riemannian Sol-manifolds in the adiabatic limit”, Siberian Math. J., 51:2 (2010), 370–382  mathnet  crossref  mathscinet  isi  elib  elib
    11. Butler L.T., “Positive-entropy integrable systems and the Toda lattice, II”, Math Proc Cambridge Philos Soc, 149:3 (2010), 491–538  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Jean-Pierre Marco, “Polynomial Entropies and Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 18:6 (2013), 623–655  mathnet  crossref  mathscinet  zmath
    13. A. Yu. Konyaev, “Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation”, Sb. Math., 205:1 (2014), 45–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. Clémence Labrousse, Jean-Pierre Marco, “Polynomial Entropies for Bott Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 19:3 (2014), 374–414  mathnet  crossref  mathscinet  zmath
    15. I. A. Bizyaev, A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and bifurcations in nonholonomic mechanics”, International Journal of Bifurcation and Chaos, 25:10 (2015), 15300–21  mathnet  crossref  isi
    16. Chen D., “Positive metric entropy arises in some nondegenerate nearly integrable systems”, J. Mod. Dyn., 11 (2017), 43–56  crossref  mathscinet  isi  scopus
    17. Bolsinov A., Bao J., “A Note About Integrable Systems on Low-Dimensional Lie Groups and Lie Algebras”, Regul. Chaotic Dyn., 24:3 (2019), 266–280  crossref  isi
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