Translation of the V. I. Arnold paper ``From superpositions to KAM theory

DOI10.1134/S1560354714060100zbMath1348.70002MaRDI QIDQ892760

Mikhail B. Sevryuk

Publication date: 12 November 2015

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

Hilbert's 13th probleminvariant tori carrying quasi-periodic motionsKAM theory and its applicationsKolmogorov as a supervisorsuperpositions of continuous functions

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Biographies, obituaries, personalia, bibliographies (01A70) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) Representation and superposition of functions (26B40) Nearly integrable Hamiltonian systems, KAM theory (70H08) History of mechanics of particles and systems (70-03)

Related Items (1)

Families of invariant tori in KAM theory: interplay of integer characteristics

Cites Work

• Remark on the paper ``On invariant curves of area-preserving mappings of an annulus
• A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
• From Hilbert's Superposition Problem to Dynamical Systems
• Cardiac arrhythmias and circle maps−A classical problem
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• The KAM Story
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• Small denominators. I. Mappings of the circumference onto itself
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Translation of the V. I. Arnold paper ``From superpositions to KAM theory