Vladimir I. Arnold

Vladimir I. Arnold - Collected Works (eBook, PDF)

Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965
Redaktion: Givental, Alexander B.; Zakalyukin, Vladimir; Viro, Oleg; Vassiliev, Victor A.; Varchenko, Alexander N.; Marsden, Jerrold E.; Khesin, Boris

• Format: PDF

Produktbeschreibung

mathematical bestsellers and integral parts of the mathematical education of students throughout the world.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 487
• Erscheinungstermin: 22. Oktober 2009
• Englisch
• ISBN-13: 9783642017421
• Artikelnr.: 37366657

Autorenporträt

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors.

Inhaltsangabe

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.

Rezensionen

"Volume II focuses on hydrodynamics, bifurcation theory and algebraic geometry. ... Arnold was a very prolific writer. The publication of his collected works is a huge task and a great service to the mathematical community particularly since his papers appeared in various journals some of which are not easily accessible. ... I have no doubt that these volumes will be of great benefit to the current and future generations of researchers and graduate students." (Gerard Misiolek, zbMATH 1354.01038, 2017)