CONTENTS -- Foreword -- References -- Acknowledgements -- Contents -- Papers -- 1. A co-chain map for the G invariant De Rham complex.. I.M. Anderson and M.E. Fels -- 1. Introduction -- 2. Lie group actions and invariant vector fields -- 3. Lie algebra cohomology -- 4. A map on the G invariant de Rham complex -- 5. The cochain condition -- 6. Examples -- References -- 2. New examples of trihamiltonian structures linking different Lenard chains C. Andrci and L. Degiovanni -- 1. Introduction -- 2. Trihamiltonian framework -- 3. Trihamiltonian extension of Toda lattice -- 4. Trihamiltonian extension of natural separable systems -- Acknowledgements -- References -- 3. Wave propagation in an elastic medium: GDS equations C. Babaoglu and S. Erbay -- 1. Introduction -- 2. Two-Dimensional Wave Packets -- 3. Special Solutions of the GDS System -- References -- 4. Parametric excitation in nonlinear dynamics T. Bakri -- 1. Introduction -- 1. Scaling and first order averaging -- 2. The periodic solutions -- 3. The Neimark-Sacker bifurcation -- 3.1. Numerical data generated by CONTENT -- 3.2. Averaging method results -- 4. Continuation of the torus -- 4.1. The averaged system -- 4.2. The original system -- 5 . Conclusions -- Acknowledgment -- References -- 5. Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 V. Bamtello -- 1. Introduction -- 2. Setting and notations -- 3. Symmetries and coercivity -- 4. Symmetry constraints for collision trajectories -- 5. Collisions with the Isosceles Symmetry -- References -- 6 . The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems S. Benenti -- 1. Posing a question -- 2. Equivalent systems -- 3. The equivalence theorem of Levi-Civita -- 4. Main theorems -- 5 . L-tensors, L-sequences, L-systems -- 6. Cofactor and bi-cofactor systems are L-systems.

References -- 7. Shadowing chains of collision orbits for the elliptic 3-body problem S. Bolotin -- 1. Introduction -- 2. Shadowing infinite collision chains -- 3. Twist map reformulation -- 4. Almost autonomous case -- References -- 8. Similarity reductions of an optical model M.S. Bruzon and M.L. Gandarias -- 1. Introduction -- 2. Lie symmetries -- 3. New exact solutions -- 4. Conclusions -- Acknowledgments -- References -- 9. Fold, transcritical and pitchfork singularities for time-reversible systems C.A. Buzzi, P.R. Silva and M.A. Teixeira -- 1. Introduction -- 2. Singularly Perturbed Reversible Vector Fields on the plane -- 3. Fold, Transcritical and Pitchfork Singularities -- References -- 10. Homographic three-body motions with positive and negative masses M. Celli -- 1. The vector of inertia -- 2. The two-body problem with M = 0 -- 3. Central and complex central configurations -- 4. Some homographic solutions -- 5. The three-body complex central configurations -- 6. A particular case of the three-body problem with M = 0 -- Acknowledgments -- References -- 11. Remarks on conformal Killing tensors and separation of variables C. Chanu and G. Rastelli -- 1. Conformal Killing tensors and separation of variables -- 2. Conformal Killing tensors and L-systems -- 2.1. K-sequences and C-sequences -- 2.2. C-sequences and L-systems -- 3. Conclusion -- Acknowledgments -- References -- 12. A regularity theory for optimal partition problems.. M. Conti, G. Verzini and S. Terracini -- 1. The functional class S -- 2. The class S in different problems of nonlinear analysis: some examples -- 2.1. Highly competing diffusion systems -- 2.2. An optimal partition problem -- 3. The regularity theory for the elements of S -- 4. Further regularity in dimension N=2 -- 4.1. Local properties of the free boundary -- Conclusions. -- References.

13. Lambda and mu-symmetries. G. Gaeta -- Introduction -- 1. Standard prolongations -- 2 . Lambda-prolongations -- 2.1. The work of Muriel and Romem -- 2.2. The work of Pucci and Saccomandi -- 2.3. The work of Momndo -- 3. Mu-prolongations -- mu-symmetries for PDEs -- 4. Mu-symmetries for systems of PDEs -- 5. Compatibility condition and gauge equivalence -- References -- 14. Potential symmetries and linearization of some evolution equations M. L. Gandarias -- 1. Introduction -- 2. Potential symmetries -- 3. Linearization -- 4 . Concluding remarks -- References -- 15. Periodic solutions for zero mass nonlinear wave equations G. Gentile -- 1. Introduction -- 1.1. The model -- 1.2. The results -- 2. General scheme -- 2.1. Lyapunov-Schmidt decomposition -- 2.2. Zero-order solution -- 2.3. Avoiding the loss of regularity -- 3. Lindstedt series method -- 3.1. Power series expansion -- 3.2. Counterterms and resummations -- References -- 16. Fundamental covariants in the invariant theory of Killing tensors J . T. Homood, R. G. McLenaghan, R. G. Smirnov and D. The -- 1. Introduction -- 2. Invariant theory of Killing tensors (ITKT) -- 3. The main result -- 4. Conclusions -- References -- 17. Global geometry of 3-body trajectories with vanishing angular momentum W. Y. Hsiang -- 1. Jacobi's reformulation of Lagrange's least action principle, a profound geometrization of mechanics -- 2. Conservation of angular momentum and the orbital geometry of ( S 0 ( 3 ) , M ) -- 3. Kinematic geometry of rn-triangles -- 4. Shape curves, cone surfaces and the geodesic equation of (M(U,h) ds2h) -- 5. Formula of VU* and a monotonicity theorem -- 6. Some problems on global geometry of geodesics in (M(U,h) da2h) -- References.

18. The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension A. Kadem -- 1. Preliminaries and examples -- 1.1. Proposition -- 1.2. Example: -- 1.3. Example: -- 2. The study of the boundary of the set of the controllable affine systems C , -- 2.1. Commentaries -- 3. Study of border cases -- 4. Main result -- 5. Conclusion -- References -- Appendix -- 19. On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure I.I. Kossenko -- 1. Equations of motion -- 2. Action-angle variables -- 3. Existence of conditionally-periodic motions -- Acknowledgments -- References -- 20. An explicit solution of the (quantum) elliptic Calogero-Sutherland model E. Langmann -- 1. Introduction -- 2. Expanding in q2 -- 3. Expanding in y -- 4. Expanding in -- 5 . Conclusions -- Acknowledgments -- References -- 21. An application of the Melnikov integral to a restricted three body problem J . Llibre and E. Perez-Chavela -- 1. Introduction and equations of motion -- 2. The main result -- Acknowledgments -- References -- 22. Reductions of integrable equations and automorphic Lie algebras S. Lombardo and A . V. Milchailov -- 1. Introduction -- 2. General rational Lax operators -- 3. The problem of reduction and the reduction group -- 3.1. Reduction group and automorphic subalgebras -- 4. DN-Reductions of sl(2, C)-Lax operators with simple poles -- 4.1. Automorphic Lie algebras corresponding t o twisted (A-dependent) automorphisms -- Acknowledgments -- References -- 23. Geometric reduction of Poisson operators.. K. Marciniak and M. Btaszak -- References -- 24. Closed manifolds admitting metrics with the same geodesics V.S. Matveev -- 1. Introduction -- 1.1. Definitions -- 1.2. History.

2. Resent results -- 3. Methods and ideas -- 3.1. Integrability fog. the geodesic flows of geodesically equivalent metrics -- 3.2. What is special in these integrals? -- 3.3. If the metrics are strictly non-proportional -- 3.4. Geodesic equivalence and zero entropy -- 3.5. General case -- Acknowledgments -- References -- 25. A transcritical-flip bifurcation in a model for a robot-arm H. G. E. Meijer -- 1. Introduction -- 2. The method -- 3. Results for a Fold-Flip bifurcation. -- 3.1. Fold-Flap -- 3.2. An example -- 4. Conclusions -- Acknowledgement -- References -- 26. Alignment and the classification of Lorentz-signature tensors R. Milson -- 1. Introduction -- 2. Alignment -- 3. Alignment polynomials -- 4. Bivectors -- 5 . Weyl-type tensors -- Acknowledgements -- References -- 27. Renormalization group symmetry and gas dynamics.. S. Murata -- 1. Introduction -- 2. RGS method to initial value problem -- 3. Perfect gas dynamics -- 4. Summary -- References -- 28. Refined computation of hypernormal forms.. J. Murdoclc -- References -- 29. New order reductions for Euler-Lagrange equations. C. Muriel and J.L. Romero -- 1. Introduction -- 2. The concept of variational C" -symmetry -- 3. Order reduction through variational Cm -symmetries -- 4. Conservation of variational symmetries by order reduct ions -- 4.1. An example -- 5. Conclusions -- References -- 30. Regularity of pseudogroup orbits.. P. J. Olver and J. Pohjanpetto -- 1. Introduction -- 2. Tameness of Lie Pseudogroups -- 3. Regularity of Orbits -- References -- 31. Relaxation times to equilibrium in Fermi-Pasta-Ulam system., S. Paleari and T. Penati -- 1. Introduction -- 2. Natural packets: Two time scales -- 3. Equipartition times -- 3.1. Numerical indicators -- 3.2. Exponentially long times t o equipartition -- 3.3. Thermodynamic limit -- 4. Further explorations -- Appendix: The model.

Acknowledgments.