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Kolmogorov seminar on selected questions of analysis

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Collected Works

Part of the book series: Vladimir I. Arnold - Collected Works ((ARNOLD,volume 1))

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Abstract

The seminar was concerned with two groups of questions.

I. Ill-posed problems in analysis and mechanics, that is, problems whose solutions are everywhere discontinuously dependent on the parameter, in the main, ‘problems with a small denominator’.

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References

  1. Bourguin, D.G., Duffin, R.:The Dirichlet problem for the vibrating string, Bull. Amer. Math. Soc. 45, 851–859 (1939).

    Article  MathSciNet  Google Scholar 

  2. John, F.: The Dirichlet problem for a hyperbolic equation. Amer. J. Math. 63, 141–154 (1941).

    Article  MathSciNet  Google Scholar 

  3. Sobolev, S.L.: An example of a well-posed boundary-value problem for the equation of a vibrating string with conditions on the whole of the boundary. Dokl. Akad. Nauk SSSR 109, 707 (1956).

    MATH  MathSciNet  Google Scholar 

  4. Aleksandryan, R.A.: On the Dirichlet problem for the string equation and the completeness of a system of functions in a disc. Dokl. Akad. Nauk SSSR 73, 869–872 (1950).

    MathSciNet  Google Scholar 

  5. Vakhaniya, R.A.: On a boundary-value problem with conditions on the whole of the boundary for a hyperbolic system equivalent to the string equation. Dokl. Akad. Nauk SSSR 116, 906–909 (1957).

    MATH  MathSciNet  Google Scholar 

  6. Vlasov, V.Z.: On the membrane theory of shells of rotation. Izv. Akad. Nauk, Ser. Tekh. Nauk No. 5, 55–84 (1955).

    MathSciNet  Google Scholar 

  7. Sokolov, A.M.: Calculation of shells of negative curvature. Izv. Akad. Nauk, Ser. Tekh. Nauk No. 5, 85–101 (1955).

    Google Scholar 

  8. Poincaré, H.: On curves defined by differential equations. Gostekhizdat, Moscow–Leningrad (1947).

    Google Scholar 

  9. Denjoy, A.: Sur les courbes, définies par les équations différentielles à la surface du tore. Journ. de Math. 11, 333 (1932).

    MATH  Google Scholar 

  10. Cremer, H.: Über die Schrödersche Funktionalgleichung und das Schwarzsche Eckenabbildungsproblem. Ber. Sacs. Acad. 84, 291–384(1932).

    Google Scholar 

  11. Siegel, C.L.: Iterations of analytic functions. Ann. of Math. No. 4, 607 (1942).

    Google Scholar 

  12. Kolmogorov, A.N.: On dynamical systems with integral invariants on the torus. Dokl. Akad. Nauk SSSR 93, 763–766 (1953).

    MATH  MathSciNet  Google Scholar 

  13. Kolmogorov, A.N.: On the preservation of conditionally periodic motion under a small variation in the Hamiltonian function. Dokl. Akad. Nauk SSSR 98, No. 4 (1954).

    Google Scholar 

  14. Kolmogorov, A.N.: General theory of dynamical systems and classical mechanics. Proc. Internationial Mathematical Congress (Amsterdam), 315–333 (1954).

    Google Scholar 

  15. Borel, E.: Le¸cons sur les fonctions monogènes. Paris (1917).

    Google Scholar 

  16. Artsimovich, L.A.: Studies in controlled thermonuclear reactors in the USSR. Usp. Fiz. Nauk SSSR 66, No. 4 (1958).

    Google Scholar 

  17. Andronov, A.A., Pontryagin L.C.: Structurally stable systems. Dokl. Akad. Nauk SSSR 14, 247–250 (1937).

    Google Scholar 

  18. Burgers, J.M.: Correlations problems in a one-dimensional model of turbulence. Proc. Akad. Sci. Amst. 53, 247–260, 393–406, 718–742 (1950).

    Google Scholar 

  19. Burgers, J.M.: Statistical problems connected with the solution of a simple non-linear partial differential equation. Proc. Akad. Sci. Amst. B57, No. 4, 403–433 (1954).

    MathSciNet  Google Scholar 

  20. Hopf, E.: Statistical hydromechanics and functional calculus. J. Rat. Mech. Analysis. 1, No.1, 87–123 (1952).

    MathSciNet  Google Scholar 

  21. Wasow, W.: One small disturbance of plane Coutte flow. J. Res. Nat. Bur. Stand. 51. 195–202 (1953).

    MATH  MathSciNet  Google Scholar 

  22. Wasow, W.: Asymptotic solution of the differential equation of hydrodynamic stability in a domain containing a transition point. Ann. Math. 58, 222– 252(1953).

    Article  MathSciNet  Google Scholar 

  23. Lin, C.C.: The theory of hydrodynamic stability. Cambridge University Press, Cambridge (1955).

    MATH  Google Scholar 

  24. Petrov, G.I.: Application of Galerkin’s method to the problem of the stability of the flow of a viscous liquid. Prikl. Mat. Mekh. 4, No. 3 (1940).

    Google Scholar 

  25. N.I. Pol’ski?, On the convergence of certain methods of analysis, Ukr. Mat. Zh. 7, No. 1 (1955), 56–70.

    Google Scholar 

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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, 94720-3840, Berkeley, CA, USA

    Alexander B. Givental

  2. Department of Mathematics, University of Toronto, M5S 3G3, Toronto, ON, Canada

    Boris A. Khesin

  3. Control & Dynamical Systems and Applied & Computational Mathematics, California Institute of Technology, 91125-8100, Pasadena, CA, USA

    Jerrold E. Marsden

  4. Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA

    Alexander N. Varchenko

  5. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russian Federation

    Oleg Ya. Viro

  6. Institute of Mathematical Sciences, Stony Brook University, 11794-3660, Stony Brook, NY, USA

    Vladimir M. Zakalyukin

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(2009). Kolmogorov seminar on selected questions of analysis. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_8

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