Mechanics, Analysis and Geometry: 200 Years after Lagrange

Edited By

  • M. Francaviglia, Institute for Mathematical Physics, "J.-Louis Lagrange", University of Torino, Italy

Providing a logically balanced and authoritative account of the different branches and problems of mathematical physics that Lagrange studied and developed, this volume presents up-to-date developments in differential goemetry, dynamical systems, the calculus of variations, and celestial and analytical mechanics.
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Book information

  • Published: February 1991
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-88958-4

Table of Contents

Foreword. Dynamical Systems. Periodic solutions near the Lagrange equilibrium points in the restricted three-body problem for mass ratios near Routh's critical value (G. Dell'Antonio). Lower bound on the dimension of the attractor for the Navier-Stokes equations in Space Dimension 3 (J.-M. Ghidaglia and R. Temam). Homoclinic chaos for ray optics in a fiber: 200 years after Lagrange (D.D. Holm and G. Kovacic). On the vortex-wave system (C. Marchioro and M. Pulvirenti). Integrable Systems and Quantum Groups. The averaging procedure for the soliton-like solutions of integrable systems (I.M. Krichever). A new topological invariant of topological Hamiltonian systems of differential equations and applications to problems in physics and mechanics (A.T. Fomenko). On the Lie algebra of motion integrals for two-dimensional hydrodynamic equations in Clebsh variables (V.E. Zakharov). Quasiclassical limit of quantum matrix groups (B.A. Kupershmidt). Analytical Mechanics and Calculus of Variations. A multisymplectic framework for classical field theory and the calculus of variations: I. Covariant Hamiltonian formalism (M.J. Gotay). Conformal symmetries and generalized recurrences for heat and Schrödinger equations in one spatial dimension (E.G. Kalnins, R.D. Levine and W. Miller, Jr.). On the geometry of the Lagrange problem (W.F. Shadwick). Global Analysis. Massivité des espaces de Sobolev et spectre du Laplacien des Variétés Riemanniennes compactes (A. Avez). Yang-Mills fields on Lorentzian manifolds (Y. Choquet-Bruhat). Eigenvalues of the Laplacian (T.M. Rassias). Differential Geometry. How can a drum change shape, while sounding the same? Part II (D. DeTurck, H. Gluck, C. Gordon and D. Webb). Vector fields on the circle (N. Hitchin). Scalar differential invariants, diffieties and characteristic classes (A.M. Vinogradov). Relativity and Field Theory. The covariant phase space of asymptotically flat gravitational fields (A. Ashtekar, L. Bombelli and O. Reula). The Lagrangian approach to conserved quantities in general relativity (M. Ferraris and M. Francaviglia). Differential geometry and the Lagrangians of superstring theory (P. Frè). Quantum gravity and quantum groups (J.E. Nelson and T. Regge). Chen's iterated path integrals, quantum vortices and link invariants (V. Penna, M. Rasetti and M. Spera). Massive modes and effective geometry (K.S. Stelle). History of Mathematics. Formal versus convergent power series (J. Dieudonné).