CONTENTS -- Foreword -- Acknowledgements -- The Mumford representation for a hyperelliptically separable system with deficiency -- References -- An outline of the geometrical theory of the separation of variables in the Hamilton-Jacobi and Schrodinger equations -- 1. About the definition of separation -- 2. Separable webs -- 3. First integrals -- 4. The separation of the Schrodinger equation -- References -- Eigenvalues of Killing tensors and orthogonal separable webs -- 1. Introduction -- 2. The Eisenhart-Killing equations and the cases n = 2 and n = 3 -- 3. The general case -- 4. Illustrative examples -- References -- Partial symmetries and symmetric sets of solutions to PDE's -- 1. Introduction -- 2. Partial symmetries -- 3. Partial symmetries and symmetric sets: Examples -- References -- On the algebro-geometric solution of 3 x 3 matrix Riemann-Hilbert problem -- 1. Introduction -- 2. Homology basis and holomorphic differentials -- 3. Derivation of the solution the RH-problem -- References -- Bi-Hamiltonian geometry and separation of variables for Gaudin models: A case study -- 1. Introduction -- 2. The model and the bi-Hamiltonian structure -- 3. The GZ analysis of the Poisson pencil -- 4. On Separation of Variables -- References -- Bifurcations in flow-induced vibration -- 1. Introduction -- 2. The Model -- 3. Conditions for Vibration Cancellation -- 4. Dynamics of the full System -- 5. Conclusion -- References -- Steklov-Lyapunov type systems -- 1. Introduction. Gaudin magnets and the hierarchy of the Steklov-Lyapunov systems -- 2. Special rank r coadjoint orbits in so(m) x so(m) -- 3. Rank 2 case -- References -- Quaternionic integrable systems -- 1. Introduction. Standard integrable systems -- 2. Generalizations: Clifford dynamics -- 3. Quaternionic integrable systems -- 4. Hyperhamiltonian dynamics.

5. Example. The Pauli spin equation -- 6. Some final comments -- References -- Renormalization group and summation of divergent series for hyperbolic invariant tori -- 1. Introduction and results -- 2. Perturbation theory and tree expansion -- 3. Accumulation of small divisors and summations -- 4. Conclusions and conjectures -- References -- Numerical study of stability of non-chaotic patterns in coupled map lattices -- 1. Introduction -- 2. Small coupling -- 3. Medium and large coupling -- References -- Quasi-exact solvability and Calogero-Sutherland models -- 1. Introduction -- 2. A new family of Dunkl operators -- 3. Construction of the Hamiltonian -- 4. Classification of the models -- References -- On the linearization of holomorphic vector fields in the Siegel domain with linear parts having nontrivial Jordan blocks -- 1. Introduction -- 2. Spaces of power series -- 3. Divergent transformations for vector fields in C3 -- 4. Convergent transformations for vector fields in Cn n > 4 -- References -- Matrix integrals as Borel sums of Schur function expansions -- 1. Introduction r-functions related to Schur functions -- 2. Relation between FM(t t*) and matrix integrals -- References -- Smooth normalization of a vector field near an invariant manifold -- Introduction -- 1. Basic notions -- 2. Lyapunov type exponents -- 3. Invariant manifolds and foliations -- 4. Normal form theorem -- 5. Deformation method -- 6. Special smooth section theorem -- 7. Flatness lemma -- 8. Proof of Theorem 4.1 -- References -- Inverse problems for SL(2) Lattices -- 1. Introduction -- 2. Quadratic r-matrix algebra and the model -- 3. Separation representation -- 4. Lattice representation -- 5. Inverse problem -- 6. Generating function -- 7. Integrable DST model -- 8. Periodic Toda lattice -- References.

Group invariants of Killing tensors in the Minkowski plane -- 1. Introduction -- 2. Induced Isometry of K2(R21) -- 3. Group-Invariant Classification of Orthogonal Separable Coordinates in R21 -- 4. Conclusions -- References -- Some remarks about the geometry of Hamiltonian conservation laws -- 1. Introduction -- 2. The dissipative case -- 3. The Hamiltonian case -- 4. The distribution theoretical approach -- 5. Another related developments -- 6. Future directions and work in progress -- References -- Janet's algorithm -- 1. Introduction -- 2. The basic duality -- 3. Solutions -- 4. Compatibility conditions and syzygies -- References -- Some integrable billiards -- 1. Introduction -- 2. Great and little -- 3. Related constructions -- 4. Reality conditions -- References -- On Separable systems in two dimensions -- 1. Introduction -- 2. Preliminary material -- 3. Main result -- 4. Remarks and conclusions -- References -- Classical and nonclassical symmetry reductions of the Schwarz-Korteweg-de Vries equation in (2+1) dimensions -- 1. Introduction -- 2. Lie symmetries -- 3. Nonclassical symmetries -- 4. Conclusions -- References -- Traveling waves and monodromy in anharmonic lattices -- 1. Anharmonic lattices -- 2. Normal modes -- 3. The Birkhoff normal form -- 4. Example: the Fermi Pasta Ulam lattice -- References -- Symmetries of relative equilibria for simple mechanical systems -- 1. Introduction -- 2. Symmetries of the relative equilibria of a simple mechanical system -- 3. Symmetries of relative equilibria for the affine rigid body model -- References -- A spectral sequence approach to normal forms -- 1. Introduction -- 2. Formal definitions -- 3. The anharmonic oscillator -- 4. Concluding remarks -- References.

Rational parametrization of strata in orbit spaces of compact linear groups -- 1. Introduction -- 2. Parametrization of strata in orbit spaces of compact linear groups -- 3. An Example -- References -- Effective hamiltonians and perturbation theory for quantum bound states of nuclear motion in molecules -- 1. Global and Local methods of quantum mechanical calculations -- 2. Perturbation Theory ( Contact Transformations ) and Effective Hamiltonians -- 3. Near degenerate states. Accidental resonances -- 4. Strong coupling of molecular Vibrations and Rotation -- References -- Branches of invariant tori and rotation numbers in symmetric hamiltonian systems: An example -- 1. Introduction -- 2. Relative equilibria -- 3. Symmetry reduction -- 4. Sub harmonic bifurcation -- 5. Rotation numbers along the bridges -- References -- Generalized Hasimoto transformation and vector sine-Gordon equation -- 1. Introduction -- 2. Hasimoto transformation -- References -- Conference program -- List of participants -- Papers appearing in previous SPT proceedings.