Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical SystemsV.I. Arnol'd, S.P. Novikov A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems. |
Contents
| 1 | |
| 83 | |
Integrable Systems and FiniteDimensional Lie Algebras | 87 |
GroupTheoretical Methods in the Theory of FiniteDimensional Integrable Systems | 116 |
Quantization of Open Toda Lattices | 226 |
Other editions - View all
Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems V.I. Arnol'd,S.P. Novikov No preview available - 2010 |
Dynamical Systems VII: Integrable Systems Nonholonomic Dynamical Systems V.I. Arnol'd,S.P. Novikov No preview available - 2014 |
Common terms and phrases
action of G affine Lie algebras algebra g automorphism Bott integral canonical Cartan coadjoint orbits codimension commutative compact completely integrable connected consider construction corresponding curve decomposition defined Definition denote described diffeomorphic differential distribution dual Dynamical Systems English transl fiber finite-dimensional Fomenko geodesic flow geometry given graph h₁ Hamiltonian systems Heisenberg group homeomorphic integrable systems invariant isomorphic lattice Lax equations Lax matrix Lax pair left-invariant Let g Lie group Lie group G linear Liouville loop algebras mapping Math metric moment map n₁ nilpotent nonholonomic geodesic flow operators Perelomov Phys Poisson bracket Poisson structure polynomial problem Proposition quantum quotient R-bracket R-matrix reduction representation respect Reyman rigid body root Section Semenov-Tian-Shansky semisimple Lie algebra sgrad Sklyanin smooth spectral subalgebra subgroup submanifold subspace symmetric spaces symplectic manifold Theorem theory Toda lattice tori torus Trofimov V₁ V₂ vector fields
Popular passages
Page 261 - Geometric and algebraic mechanisms of the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras, Itogi Nauki i Tekhniki: Sovremennye Problemy Mat.: Fundamental