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Vladimir I. Arnold - Collected Works

Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965

  • Book
  • © 2009

Overview

Authors:
  1. Vladimir I. Arnold

    1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russian Federation

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Editors:
  1. Alexander B. Givental

    1. Department of Mathematics, University of California, Berkeley, USA

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  2. Boris A. Khesin

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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  3. Jerrold E. Marsden

    1. Control & Dynamical Systems and Applied & Computational Mathematics, California Institute of Technology, Pasadena, USA

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  4. Alexander N. Varchenko

    1. Department of Mathematics, University of North Carolina, Chapel Hill, USA

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  5. Victor A. Vassiliev
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  6. Oleg Ya. Viro

    1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russian Federation

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  7. Vladimir M. Zakalyukin

    1. Institute of Mathematical Sciences, Stony Brook University, Stony Brook, USA

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  • Collected Works of one of the most outstanding mathematicians of all times.

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

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Table of contents (32 chapters)

  1. Front Matter

    Pages I-XIII
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  2. On the representation of functions of two variables in the form χ[φ(x) + ψ(y)]

    Pages 1-4

  3. On functions of three variables

    Pages 5-8

  4. The mathematics workshop for schools at Moscow State University

    Pages 9-14

  5. The school mathematics circle at Moscow State University: harmonic functions

    Pages 15-24

  6. On the representation of functions of several variables as a superposition of functions of a smaller number of variables

    Pages 25-46

  7. Representation of continuous functions of three variables by the superposition of continuous functions of two variables

    Pages 47-133

  8. Some questions of approximation and representation of functions

    Pages 134-143

  9. Kolmogorov seminar on selected questions of analysis

    Pages 144-148

  10. On analytic maps of the circle onto itself

    Pages 149-151

  11. Small denominators. I. Mapping of the circumference onto itself

    Pages 152-223

  12. The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case

    Pages 224-226

  13. Generation of almost periodic motion from a family of periodic motions

    Pages 227-229

  14. Some remarks on flows of line elements and frames

    Pages 230-232

  15. A test for nomographic representability using Decartes’ rectilinear abacus

    Pages 233-235

  16. Remarks on winding numbers

    Pages 236-242

  17. On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian

    Pages 243-247

  18. Small perturbations of the automorphisms of the torus

    Pages 248-252

  19. The classical theory of perturbations and the problem of stability of planetary systems

    Pages 253-257

  20. Letter to the editor

    Pages 258-258
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Keywords

Authors, Editors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Alexander B. Givental

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Boris A. Khesin

  • Control & Dynamical Systems and Applied & Computational Mathematics, California Institute of Technology, Pasadena, USA

    Jerrold E. Marsden

  • Department of Mathematics, University of North Carolina, Chapel Hill, USA

    Alexander N. Varchenko

  • Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russian Federation

    Oleg Ya. Viro, Vladimir I. Arnold

  • Institute of Mathematical Sciences, Stony Brook University, Stony Brook, USA

    Vladimir M. Zakalyukin

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