Dynamical Systems IV: Symplectic Geometry and Its ApplicationsS.P. Novikov This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field. |
Contents
Contents | 5 |
3 Families of Quadratic Hamiltonians | 11 |
4 The Symplectic Group | 17 |
Copyright | |
14 other sections not shown
Other editions - View all
Dynamical Systems IV: Symplectic Geometry and its Applications V.I. Arnol'd,S.P. Novikov No preview available - 2001 |
Common terms and phrases
A₁ action algebraic-geometric analogue arbitrary boundary called canonical caustics characteristic coadjoint cobordism coefficients cohomology commuting compact complex connected construction contact structure Corollary corresponding cotangent bundle critical points curve defined deformation diffeomorphic differential dimension eigenvalues English translation equal equivalent Euclidean example F₁ fibration fibre finite gap finite-gap formula front geodesic geometric germs Grassmann manifold group G Hamiltonian system hydrodynamic type hyperplane hypersurface integral invariant inverse isomorphic KdV equation Lagrangian fibration Lagrangian submanifold lattice Lemma Let us consider Lie algebra Lie group linear Math matrix metric neighbourhood obtained operator orbit P₁ P₂ parameter phase space Poisson bracket Poisson structure polarization poles polynomials potential prequantization problem quadratic Hamiltonians quantization representation Riemann surface Schrödinger sect singularities solutions spectral subspace symplectic group symplectic manifold symplectic space symplectic structure symplectomorphism Theorem theory torus transformation two-dimensional variables vector field w₁ zero