Global Aspects of Classical Integrable Systems

By R. Cushman, L. Bates. 2004

514 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2a633f3334ecc5de0673f3a2099374ac24fc9032

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Symplectic theory of completely integrable Hamiltonian systems (2011, background): “ out by many authors, including Marsden, Ratiu and their collaborators. The semiclassical aspects of integrable systems have been recently studied in the book [110] and the article [109]. In the book [26] singular Lagrangian ﬁbrations are treated from the point of view of classical mechanics. Finall”
Quantum control of molecular rotation (2018, methodology): “The two systems are known as the Euler top and the Lagrange top in mathematics and have been studied for many centuries (Cushman and Bates, 1997).”
Normal linear stability of quasi-periodic tori (2007, methodology): “The Hamiltonian 1 : −1 resonance is of interest, since it is observed in many mechanical systems including the Lagrange top [34,35], the double spherical pendulum [63], the restricted three body problem [64] and the 3D Hénon–Heiles family as this models the movement of galaxies [38,46,47].”
Continuation of periodic orbits in conservative and Hamiltonian systems (2003, methodology): “Following Cushman and Bates [5] we define a mapping w : C2 → R3 by w1 = w1(z) := i(ab̄ − āb), w2 = w2(z) := ab̄ + āb, w3 = w3(z) := aā − bb̄, ∀z = (a, b) ∈ C2; (8.11) together with F (z) the scalar functions w1(z), w2(z) and w3(z) form a basis for the quadratic invariants under the S1-action on C”
Singular reduction of implicit Hamiltonian systems (2003, methodology): “Define the set of smooth functions on M0 as follows (see [9], or for the original source see [25]).”
Superintegrable Hamiltonian Systems: Geometry and Perturbations (2005, background): “Monodromy has been identified in several Liouville integrable systems, see, e.g., [ 14 ], and plays an important role in their quantization, see, e.g., [46, 15] and references therein.”
Symplectic Topology of Integrable Hamiltonian Systems, II: Topological Classification (2000, methodology): “us interesting examples. 2. Regular Lagrangian torus foliations This Section is based on the works of Duistermaat [15] and Dazord and Delzant [11] (see also Boucetta and Molino [7], Cushman and Bates [9], and Marle [23]). 2.1. Action-angle coordinates. Let π : (M2n,ω,L) → On be a regular Lagrangian ”