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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 675–711 (Mi izv1200)  

This article is cited in 9 scientific papers (total in 9 papers)

Closed geodesics, asymptotic volume, and characteristics of group growth

I. K. Babenko


Abstract: A function $N_g(t)$ equal to the number of closed geodesics of length not greater than $t$ is considered on the Riemannian manifold $(M,g)$. Also considered are related questions on the behavior of the volume function for a geodesic ball on the universal covering manifold.
Bibliography: 20 titles.

Full text: PDF file (5092 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 1–37

Bibliographic databases:

UDC: 514.774.8
MSC: 53C22
Received: 04.01.1987

Citation: I. K. Babenko, “Closed geodesics, asymptotic volume, and characteristics of group growth”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 675–711; Math. USSR-Izv., 33:1 (1989), 1–37

Citation in format AMSBIB
\Bibitem{Bab88}
\by I.~K.~Babenko
\paper Closed geodesics, asymptotic volume, and characteristics of group growth
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 4
\pages 675--711
\mathnet{http://mi.mathnet.ru/izv1200}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=966980}
\zmath{https://zbmath.org/?q=an:0668.53032|0657.53024}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 1--37
\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000811}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. K. Babenko, “On the behavior of trajectories of scattering billiards on the flat torus”, Math. USSR-Sb., 72:1 (1992), 207–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. K. Babenko, “Asymptotic invariants of smooth manifolds”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 1–38  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. G. Besson, G. Courtois, S. Gallot, “Entropies et rigidités des espaces localement symétriques de courbure strictement négative”, GAFA Geom funct anal, 5:5 (1995), 731  crossref  mathscinet  zmath
    4. Gérard Besson, Gilles Courtois, Sylvestre Gallot, “Minimal entropy and Mostow's rigidity theorems”, Ergod Th Dynam Sys, 16:4 (1996)  crossref
    5. R. I. Grigorchuk, “Weight functions on groups and an amenability criterion for Beurling algebras”, Math. Notes, 60:3 (1996), 274–282  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. R. Grigorchuk, P. Harpe, “On problems related to growth, entropy, and spectrum in group theory”, J Dyn Control Syst, 3:1 (1997), 51  crossref  mathscinet  zmath  elib
    7. V. V. Dontsov, “Systoles on Heisenberg groups with Carnot–Carathéodory metrics”, Sb. Math., 192:3 (2001), 347–374  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Charles H. Conley, “Conformal symbols and the action of contact vector fields over the superline”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2009:633 (2009), 115  crossref
    9. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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