Symmetry And Perturbation Theory (Spt 2001), Proceedings Of The International Conference SPT 2001

The third conference on "Symmetry and Perturbation Theory" (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field - more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit. Contents: Geometry and Dynamics of Hyperelliptically Separable Systems (S Abenda) A Functional Analysis Approach to Arnold Diffusion (M Berti) Linearizing Resonant Normal Forms (G Gaeta) Tori Breakdown in Coupled Map Lattices (C Gibe Geometry and dynamics of hyperelliptically separable systems / S. Abenda -- Multiple Hopf bifurcation in problems with O(2) symmetry: Kuramoto-Sivashinski equation / F. Amdjadi -- Sternberg-Chen theorem for equivariant Hamiltonian vector fields / G.R. Belitskii and A. Ya. Kopanskii -- A functional analysis approach to Arnold diffusion / M. Berti -- The symplectic Evans matrix and solitary wave instability / T. Bridges and G. Derks -- Classical symmetries for a Boussinesq equation with nonlinear dispersion / M.S. Bruzon, M.L. Gandarias and J. Ramirez -- Pseudo-normal forms and their applications / A. Delshams and J. Tomas Lazaro -- Periodic orbits of Langmuir's atom / F. Diacu and E. Perez-Chavela -- Heteroclinic cycles and wreath product symmetries / A.P.S. Dias, B. Dionne and I. Stewart -- Linearizing resonant normal forms / G. Gaeta -- Symmetry analysis and reduction of the Schwarz-Korteweg-De Vries equation in (2 + 1) dimensions / M.L. Gandarias, M.S. Bruzon and J. Ramirez -- Tori breakdown in coupled map lattices / C. Giberti -- Evolution of the universe in two Higgs-doublets standard models / Yu. M. Gufan [und weitere] -- Possible ground states of D-wave condensates in isotropic space through geometric invariant theory / Yu. M. Gufan [und weitere] -- Possible ground states of D-wave condensates in isotropic space through geometric invariant theory / Yu. M. Gufan [und weitere] -- Parent phase as a zero approximation in phase transition theory / Yu. M. Gufan, I.A. Sergienko and M.B. Stryukov -- Symmetry and reduction of the 2 + 1 dimensional variable coefficient Burgers equation / F. Gungor -- A two-dimensional version of the Camassa-Holm equation / H.-P. Kruse. J. Scheurle and W. Du -- C[symbol] symmetries and equations with symmetry algebra SL(2,R) / C. Muriel and J.L. Romero -- Generalizations of Gordon's theorem / N. Nekhoroshev -- Moving frames: A brief survey / P.J. Olver -- Critical point theory and Hamiltonian dynamics around critical elements / J.-P. Ortega and T.S. Ratiu -- Computing invariant manifolds of perturbed dynamical systems / J. Palacian and P. Yanguas -- Periodic solutions for resonant nonlinear PDEs / S. Paleari -- A symmetric normal form for the fermi pasta ulam chain / B. Rink -- One dimensional infinite symmetries, boundary conditions, and locol conservation laws / V. Rosenhaus -- Normal forms, geometry, and dynamics of atomic and molecular systems with symmetry / D. Sadovskii -- Higher order resonance in two degrees of freedom Hamiltonian system / J.M. Tuwankotta and F. Verhulst -- Stability of Hamiltonian relative equilibria by energy methods / C. Wulff, G. Patrick and M. Roberts -- Topologically unavoidable degeneracies in band structure of solids / J. Zak -- Symmetry, perturbation theory, and Louis Michel / B. Zhilinskii -- Conference program -- List of participants -- List of tutorial papers -- SPT98 -- SPT96

In August/September 2000, a group of 80 physicists from 53 laboratories in 15 countries met in Erice, Italy, to participate in the 38th Course of the International School of Subnuclear Physics. This book constitutes the proceedings of that meeting. It focuses on the theoretical investigation of several basic unity issues, including: (1) the understanding of gauge theories in both their continuum and lattice versions; (2) the possible existence and relevance of large extra dimensions together with the resultant lowering of the Planck/string scale to the TeV range; (3) the origin and structure of flavour mixing in the quark and lepton (neutrino) sectors.

Many classical integrable systems (like the Euler, Lagrange and Kowalewski tops or the Neumann system) as well as finite dimensional reductions of many integrable PDEs share the property of being algebraically completely integrable systems.