RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1993, Volume 48, Issue 4(292), Pages 3–130 (Mi umn1314)  

This article is cited in 23 scientific papers (total in 24 papers)

Statistical properties of the spectra of Laplace–Beltrami operators on Liouville surfaces

D. V. Kosygina, A. A. Minasovb, Ya. G. Sinaic

a M. V. Lomonosov Moscow State University
b Princeton University, Department of Mathematics
c L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full text: PDF file (5607 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1993, 48:4, 1–142

Bibliographic databases:

UDC: 517.984
MSC: 81R15, 81R12, 47B40, 47A75
Received: 09.06.1993

Citation: D. V. Kosygin, A. A. Minasov, Ya. G. Sinai, “Statistical properties of the spectra of Laplace–Beltrami operators on Liouville surfaces”, Uspekhi Mat. Nauk, 48:4(292) (1993), 3–130; Russian Math. Surveys, 48:4 (1993), 1–142

Citation in format AMSBIB
\Bibitem{KosMinSin93}
\by D.~V.~Kosygin, A.~A.~Minasov, Ya.~G.~Sinai
\paper Statistical properties of the spectra of Laplace--Beltrami operators on Liouville surfaces
\jour Uspekhi Mat. Nauk
\yr 1993
\vol 48
\issue 4(292)
\pages 3--130
\mathnet{http://mi.mathnet.ru/umn1314}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1257884}
\zmath{https://zbmath.org/?q=an:0838.58041}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993RuMaS..48....1M}
\transl
\jour Russian Math. Surveys
\yr 1993
\vol 48
\issue 4
\pages 1--142
\crossref{https://doi.org/10.1070/RM1993v048n04ABEH001052}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993NY15100001}


Linking options:
  • http://mi.mathnet.ru/eng/umn1314
  • http://mi.mathnet.ru/eng/umn/v48/i4/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Ya. B. Vorobets, “Asymptotics of the spectrum of the Laplace–Beltrami operator on tori with Liouville and infra-Liouville metrics”, Russian Math. Surveys, 52:2 (1997), 430–431  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Holger Waalkens, Jan Wiersig, Holger R. Dullin, “Elliptic Quantum Billiard”, Annals of Physics, 260:1 (1997), 50  crossref
    4. V. S. Matveev, “The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities”, Math. Notes, 64:3 (1998), 357–363  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. H. Alt, A. Bäcker, C. Dembowski, H.-D. Gräf, R. Hofferbert, “Mode fluctuation distribution for spectra of superconducting microwave billiards”, Phys. Rev. E, 58:2 (1998), 1737  crossref
    6. D. A. Popov, “On the number of lattice points in three-dimensional solids of revolution”, Izv. Math., 64:2 (2000), 343–361  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. S. Yu. Dobrokhotov, A. I. Shafarevich, “Tunnel Splitting of the Spectrum of the Beltrami–Laplace Operators on Two-Dimensional Surfaces with Square Integrable Geodesic Flow”, Funct. Anal. Appl., 34:2 (2000), 133–134  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. D. Jakobson, N. S. Nadirashvili, J. Toth, “Geometric properties of eigenfunctions”, Russian Math. Surveys, 56:6 (2001), 1085–1105  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Bruning, J, “The spectral asymptotics of the two-dimensional Schrodinger operator with a strong magnetic field. II”, Russian Journal of Mathematical Physics, 9:4 (2002), 400  mathscinet  isi
    10. Bruning, J, “The spectral asymptotics of the two-dimensional Schrodinger operator with a strong magnetic field. I”, Russian Journal of Mathematical Physics, 9:1 (2002), 14  mathscinet  isi
    11. Galya Blum, Sven Gnutzmann, Uzy Smilansky, “Nodal Domains Statistics: A Criterion for Quantum Chaos”, Phys. Rev. Lett, 88:11 (2002)  crossref
    12. L. D. Pustyl'nikov, “The quantum chaos conjecture and generalized continued fractions”, Sb. Math., 194:4 (2003), 575–587  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. A. I. Shtern, “Almost periodic functions and representations in locally convex spaces”, Russian Math. Surveys, 60:3 (2005), 489–557  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. D. A. Popov, “Remarks on uniform combined estimates of oscillatory integrals with simple singularities”, Izv. Math., 72:4 (2008), 793–816  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. D. A. Popov, “Asymptotic behaviour of the positive spectrum of a family of periodic Sturm–Liouville problems under continuous passage from a definite problem to an indefinite one”, Izv. Math., 73:3 (2009), 579–610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Hugues Lapointe, Iosif Polterovich, Yuri Safarov, “Average Growth of the Spectral Function on a Riemannian Manifold”, Communications in Partial Differential Equations, 34:6 (2009), 581  crossref
    17. Lapointe H., “A Remainder Estimate for Weyl's Law on Liouville Tori”, Spectrum and Dynamics, Crm Proceedings & Lecture Notes, 52, 2010, 89–114  isi
    18. D. A. Popov, “On the second term in the Weyl formula for the spectrum of the Laplace operator on the two-dimensional torus and the number of integer points in spectral domains”, Izv. Math., 75:5 (2011), 1007–1045  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. D. A. Popov, “Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus $g>1$”, Funct. Anal. Appl., 46:2 (2012), 133–146  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. L. D. Pustyl'nikov, “Energy Levels of Quantum Periodic Systems and Quantum Chaos”, Preprinty IPM im. M. V. Keldysha, 2014, 027, 8 pp.  mathnet
    21. D. A. Popov, “On the Weyl Formula for the Laplace Operator on Hyperbolic Riemann Surfaces”, Funct. Anal. Appl., 48:2 (2014), 150–153  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. L. D. Pustylnikov, “O gipoteze kvantovogo khaosa i obobschennykh tsepnykh drobyakh”, Preprinty IPM im. M. V. Keldysha, 2015, 037, 12 pp.  mathnet
    23. A. Yu. Anikin, S. Yu. Dobrokhotov, M. I. Katsnel'son, “Lower part of the spectrum for the two-dimensional Schrödinger operator periodic in one variable and application to quantum dimers”, Theoret. and Math. Phys., 188:2 (2016), 1210–1235  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    24. S. Yu. Dobrokhotov, D. S. Minenkov, S. B. Shlosman, “Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber”, Theoret. and Math. Phys., 197:2 (2018), 1626–1634  mathnet  crossref  crossref  adsnasa  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:661
    Full text:228
    References:59
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019