CONTENTS -- Preface -- Acknowledgements -- Geometry and Dynamics of Hyperelliptically Separable Systems -- References -- Multiple Hopf Bifurcation in Problems with O(2) Symmetry: Kuramoto-Sivashinky Equation -- Abstract -- 1 Introduction -- 2 Analysis of the Problem -- 3 Application of the Method to the Kuramoto Sivashinsky Equation -- References -- Sternberg-Chen Theorem for Equivariant Hamiltonian Vector Fields -- Introduction -- 1 Definitions -- 2 Main result -- 3 Deformation method -- 4 B-equivariant conjugacy -- References -- A Functional Analysis Approach to Arnold Diffusion -- References -- The Symplectic Evans Matrix and Solitary Wave Instability -- References -- Classical Symmetries for a Boussinesq Equation with Nonlinear Dispersion -- 1 Introduction -- 2 Lie Symmetries -- 3 Optimal system and symmetry reductions -- 4 Travelling wave solutions -- 5 Conclusions -- References -- Pseudo-Normal Forms and their Applications -- Introduction and Main Results -- References -- Periodic Orbits of Langmuir's Atom -- Heteroclinic Cycles and Wreath Product Symmetries -- References -- Linearizing Resonant Normal Forms -- Introduction -- 1 Normal forms -- 2 Map to a linear system -- 3 Integration of normal forms -- References -- Symmetry Analysis and Reductions of the Schwarz-Korteweg-De Vries Equation in (2 + 1) Dimensions -- 1 Introduction -- 2 Lie symmetries -- 3 Optimal systems and reductions -- 4 Invariance analysis of the (1 + 1)-dimensional systems -- 5 Some explicit solutions -- 6 Conclusions -- References -- Tori Breakdown in Coupled Map Lattices -- Abstract of the communication -- References -- Evolution of the Universe in Two Higgs-Doublets Standard Models -- 1 Introduction -- 2 Model 1 -- 3 Model 2 -- 4 Model 3 -- 5 Completing Model 3: Model 4 -- 6 Conclusions -- References.

Possible Ground States of D-Wave Condensates in Isotropic Space through Geometric Invariant Theory -- 1 Introduction -- 2 Physical motivations -- 3 The orbit space approach -- 4 Symmetry of the allowed D-wave condensate states in isotropic space -- References -- Parent Phase as a Zero Approximation in Phase Transition Theory -- 1 The concept of parent phase -- 2 Actual crystal structures of PrAlO3 -- 3 Minimal number of phenomenological parameters accounting for the 205 K phase transition -- 4 Parent phase approximation -- 5 Correlation between the EPR lines of the rhombohedral and orthorhombic phases -- References -- Symmetries and Reductions of the 2+ 1-Dimensional Variable Coefficient Burgers Equation -- 1 Introduction -- 2 The Symmetry Group -- 3 Reductions to ODEs -- References -- A Two-Dimensional Version of the Camassa-Holm Equation -- 1 Introduction -- 2 Euler-Poincaré Equations -- 3 Derivation of the higher-dimensional Camassa-Holm equations -- 4 Some properties of the two-dimensional Camassa-Holm equations -- 5 Numerical treatment of the equations -- References -- C∞-Symmetries and Equations with Symmetry Algebra SL(2,R) -- 1 Introduction -- 2 C∞-Symmetries and ordinary differential equations -- 3 C∞-Symmetries and conservation of symmetries for the Lie algebra sl(2,R). -- 4 General method to reduce equations admitting sl(2,R). -- 5 Classification of equations -- 6 Conclusions -- References -- Generalizations of Gordon's Theorem -- Introduction -- 1 Background -- 2 Gordon's theorem -- 3 Generalizations of Gordon's theorem -- 4 About proofs -- References -- Moving Frames: A Brief Survey -- References -- Critical Point Theory and Hamiltonian Dynamics around Critical Elements -- 1 Critical point theory in the Hamiltonian symmetric context.

2 Relative equilibria and periodic orbits around non degenerate critical points -- 3 Relative periodic orbits -- 4 Further generalizations and future directions -- References -- Computing Invariant Manifolds of Perturbed Dynamical Systems -- 1 Introduction -- 2 Extending Symmetries of the Unperturbed Part -- 3 Reduction -- 4 Examples of Application -- References -- Periodic Solutions for Resonant Nonlinear PDEs -- 1 Introduction -- 2 Resonant systems -- 3 Plate equations in higher dimension -- References -- A Symmetric Normal Form for the Fermi Pasta Ulam Chain -- 1 Introduction -- 2 The linear system -- 3 Birkhoff normalisation -- 4 Discrete symmetry -- 5 The symmetric normal form -- 6 Conclusion -- References -- One Dimensional Infinite Symmetries, Boundary Conditions, and Local Conservation Laws -- 1 Introduction -- 2 Noether operator identity. First and Second Noether Theorems -- 3 Infinite symmetry algebra with arbitrary function of time -- 4 Infinite symmetry algebra with arbitrary function of a spatial variable -- 5 Equation of nonstationary transonic gas -- 6 Conclusion -- References -- Normal Forms, Geometry, and Dynamics of Atomic and Molecular Systems with Symmetry -- 1 Introduction -- 2 Tools for qualitative and dynamical analysis -- 3 Hénon-Heiles system: an illustration -- 4 Real atomic and molecular systems -- 5 Concluding remarks -- Bibliography -- Higher Order Resonance in Two Degree of Freedom Hamiltonian System -- 1 Introduction -- 2 Two degrees of freedom Hamiltonian systems at higher order resonance -- 3 The resonance domain -- 4 Geometric Integration based on a splitting method -- 5 Systems with widely separated frequencies -- 6 Discussion -- References -- Stability of Hamiltonian Relative Equilibria by Energy Methods -- 1 Introduction -- 2 Hamiltonian systems with symmetry.

3 Relative equilibria and skew product equations -- 4 Hamiltonian relative equilibria -- 5 Hamiltonian systems near group orbits -- 6 Hamiltonian relative equilibria and slice equations -- 7 G-stability of Hamiltonian relative equilibria -- 8 A-stability of Hamiltonian relative equlibria -- 9 Conclusion -- References -- Topologically Unavoidable Degeneracies in Band Structure of Solids -- References -- Symmetry, Perturbation Theory, and Louis Michel -- References -- Conference Program -- List of Participants -- List of Tutorial Papers -- Symmetry and Perturbation Theory - SPT 98 International Workshop - Roma 16-22/12/1998 -- Symmetry and Perturbation Theory Workshop - Torino 15-20/12/1996.