Kolmogorov-Arnold-Moser theory

Kolmogorov-Arnold-Moser (KAM) Theory

The Kolmogorov–Arnold–Moser theorem

This paper gives a self contained proof of the perturbation theorem for invariant tori in Hamiltonian systems by Kolmogorov, Arnold, and Moser with sharp differentiability hypotheses. The proof follows an idea outlined by Moser in [16] and, as byproducts, gives rise to uniqueness and regularity theorems for invariant tori. 1

Quantum analogue of the Kolmogorov–Arnold–Moser transition in field-induced barrier penetration in a quartic potential

Quantum signatures of the Kolmogorov–Arnold– Moser (KAM) transition from the regular to chaotic classical dynamics of a double-well oscillator in the presence of an external monochromatic field of different amplitudes are analysed in terms of the corresponding Bohmian trajectories. It is observed that the classical chaos generally enhances the quantum fluctuations, while the quantum nonclassica...

Nash-Moser Theory for Standing Water Waves

Correspondence between Calogero-Moser systems and integrable SL(N,C) Euler-Arnold tops

The equivalence between the N-particle Calogero-Moser systems and the integrable sl(N,C)-tops is shown. New rational and trigonometric classical Lax operators for these systems are found. Relations with new solutions of the classical Yang-Baxter equations for sl(N,C) are discussed. Explicit formulae for N=2,3,4 are presented.