Vladimir I. Arnold - Collected Works

Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965
2010
ISBN: 978-3-642-01741-4
Verlag: Springer

Buch, Englisch, 487 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 1042 g

Reihe: Vladimir I. Arnold - Collected Works

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

Zielgruppe

Research

Autoren/Hrsg.

Arnold, Vladimir I.

Khesin, Boris

Givental, Alexander B.

Zakalyukin, Vladimir

Varchenko, Alexander N.

Marsden, Jerrold E.

Vassiliev, Victor A.

Viro, Oleg

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

On the representation of functions of two variables in the form ?[?(x) + ?(y)].- On functions of three variables.- The mathematics workshop for schools at Moscow State University.- The school mathematics circle at Moscow State University: harmonic functions.- On the representation of functions of several variables as a superposition of functions of a smaller number of variables.- Representation of continuous functions of three variables by the superposition of continuous functions of two variables.- Some questions of approximation and representation of functions.- Kolmogorov seminar on selected questions of analysis.- On analytic maps of the circle onto itself.- Small denominators. I. Mapping of the circumference onto itself.- The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case.- Generation of almost periodic motion from a family of periodic motions.- Some remarks on flows of line elements and frames.- A test for nomographic representability using Decartes’ rectilinear abacus.- Remarks on winding numbers.- On the behavior of an adiabatic invariant under slow periodic variation of the Hamiltonian.- Small perturbations of the automorphisms of the torus.- The classical theory of perturbations and the problem of stability of planetary systems.- Letter to the editor.- Dynamical systems and group representations at the Stockholm Mathematics Congress.- Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian.- Small denominators and stability problems in classical and celestial mechanics.- Small denominators and problems of stability of motion in classical and celestial mechanics.- Uniform distribution of points on a sphereand some ergodic properties of solutions of linear ordinary differential equations in a complex region.- On a theorem of Liouville concerning integrable problems of dynamics.- Instability of dynamical systems with several degrees of freedom.- On the instability of dynamical systems with several degrees of freedom.- Errata to V.I. Arnol’d’s paper: “Small denominators. I.”.- Small denominators and the problem of stability in classical and celestial mechanics.- Stability and instability in classical mechanics.- Conditions for the applicability, and estimate of the error, of an averaging method for systems which pass through states of resonance in the course of their evolution.- On a topological property of globally canonical maps in classical mechanics.