Symmetry And Perturbation Theory: Proceedings of the International Conference SPT 2007 Otranto, Italy 2-9 June 2007

CONTENTS......Page 10
Foreword......Page 6
Acknowledgments......Page 8
FEATURED CONTRIBUTIONS......Page 16
1. Bi-Lagrangian manifolds......Page 18
2.1. Homogeneous symplectic manifolds of a semisimple Lie group......Page 20
2.2. Fundamental gradations of a (complex or real) semisimple Lie algebra g......Page 21
2.3.2. Fundamental gradations of g2......Page 22
3. Generalized Monge- AmpBre equations and effective forms on contact manifolds......Page 23
4.1. Invariant effective forms on contactifications of homogeneous symplectic manifolds......Page 24
4.2. Invariant effective forms o n homogeneous bi-Lagmngian manifolds......Page 26
References......Page 27
1. Introduction......Page 28
2. Pfaffian Systems and Superposition......Page 30
3. Darboux Integrability and Superposition......Page 33
References......Page 35
1. Introduction......Page 36
3. Cartan structure equation in symplectic geometry......Page 37
4. The geometric operators in terms of Lie bracket, Killing form and projections......Page 41
5. Reduction to scalar part......Page 42
References......Page 43
V. Barutello & S. Terracini Sangularitaes and collisions in N-body type problems......Page 44
Locally minimal and generalized solutions......Page 47
Partial collisions......Page 48
References......Page 49
1. The six steps of the aIgorithm......Page 52
2. Explanation......Page 53
3.1. The computation of the quadratic forms Qi......Page 54
3.3. The computation of the A-symbols......Page 55
3.4. The computation of the B-symbols......Page 56
3.5. The Ricci tensor......Page 57
4. How to use this example......Page 58
References......Page 59
1. Introduction to the problem......Page 60
2.1. The k : 1 resonance......Page 62
2.2. The k : 2 resonance......Page 63
References......Page 64
1. Introduction......Page 71
2. The spin-orbit model......Page 72
3. Results......Page 75
4. Mercury’s capture......Page 77
References......Page 78
1. Introduction......Page 79
2. Darboux matrix trasformation and integrability......Page 80
3.1. Coupled wave equations......Page 82
3.2. Darboux transformations......Page 84
References......Page 86
1. Introduction......Page 88
3. Reductions......Page 90
4. Minimizers......Page 92
5 . Examples......Page 93
6. Conclusions......Page 94
References......Page 95
1. Introduction and the set-up of the problem......Page 96
2. Convergent normal form for commuting singular vector fields......Page 98
3. Gevrey estimates for divergent solutions of linear homological equations......Page 101
4. Divergent NFT and centralizers for resonant vector fields......Page 104
References......Page 105
1. Introduction......Page 107
2. The mass distribution......Page 108
3. The normal form......Page 109
4. Perturbation analysis......Page 113
References......Page 114
1. Natural coverings......Page 115
2. Integrability structures......Page 116
3. Nonlocal structures......Page 118
4. Example: the dispersionless Boussinesq equation, Ref. [6]......Page 120
References......Page 122
Introduction......Page 123
1. Anomaly via Hessian......Page 124
2. Coordinate expressions......Page 125
3. Auxiliary integrals......Page 127
4. Symmetries and compatibility......Page 128
References......Page 130
1. Introduction......Page 131
2. Differential invariants......Page 132
3. Global first variation formula......Page 133
4. Natural Lagrange structures......Page 134
5 . Example: The Hilbert Lagrangian......Page 137
References......Page 138
1. Introduction......Page 139
2. Variational systems in fibred manifolds......Page 140
3. Exterior differential systems for variational equations......Page 142
4. Symmetries and conservation laws......Page 143
References......Page 146
1. Introduction......Page 147
2. Bernoulli-type polynomials and numbers of the first kind......Page 148
3. Basics on hyperfunctions......Page 151
4. Delta rational functions and polylogarithms......Page 152
References......Page 154
Introduction......Page 155
1. Preliminaries......Page 156
2. The deformed operators dp and L p......Page 158
4. Variational A-symmetries......Page 159
References......Page 161
1. Introduction......Page 163
2. Structure of Symmetry Pseudo-Group and a Covering for the Modified Khokhlov-Zabolotskaya Equation......Page 164
3. Multi-Valued Solutions of the Khokhlov-Zabolotskaya Equation......Page 168
References......Page 169
1. General conception of the considered monodromy......Page 171
2. Fractional monodromy and its explanation......Page 172
3. Explanation of the fuzziness of monodromy......Page 175
4. Formulation of the result......Page 177
References......Page 178
1. Introduction......Page 179
2. Theoretical setting......Page 181
3. DEs characterized by their Lie point symmetries......Page 183
4. DEs which are uniquely determined by Lie algebras of vector fields on Rnfm......Page 184
Acknowledgments......Page 185
References......Page 186
1. Introduction......Page 187
2. The Diffeomorphism Pseudo-Group......Page 188
3. Lie Pseudo-Groups......Page 189
4. Pseudo-Group Actions on Extended Jet Bundles......Page 190
5. Recurrence Formulae......Page 191
6. The Symbol Modules......Page 192
References......Page 195
1. Introduction......Page 196
2. Main results......Page 200
2.1. A sketch of the proof......Page 202
References......Page 203
1. Introduction......Page 204
2. Preliminaries and statement of the main results......Page 207
3. Proof of Theorem 2.1......Page 208
4. Proof of Theorems 2.2 and 2.3......Page 209
References......Page 211
1. Introduction......Page 213
2. Continuation of zeros of constrained mappings......Page 214
3. Periodic orbits in conservative systems......Page 215
4. Reversible systems......Page 217
5 . Application to N-body problems......Page 219
References......Page 220
1. Singular perturbations and slow manifolds......Page 221
2. Extension to PDEs......Page 222
3. Formulation for wave equations......Page 223
4. A nonlinear Rayleigh wave equation......Page 225
References......Page 228
1. Introduction......Page 230
2. The Two-Dimensional Case......Page 231
3. The Three-Dimensional Case......Page 234
References......Page 237
1. Introduction......Page 238
2. Singularities of energy-momentum maps and monodromy......Page 239
3. Bidromy......Page 242
References......Page 244
EXTENDED ABSTRACTS......Page 246
2. Solution of the Problem......Page 248
3. Results......Page 249
R. Alonso Blanco, G . Manno & F. Pugliese Contact geometry of parabolic Monge-Ampdre equations......Page 250
References......Page 251
K. Andriopoulos Complete symmetry groups and Lie remarkability......Page 252
References......Page 253
M. Arminjon Quantum wave equations in curved space-time wave mechanics......Page 254
References......Page 255
1. Introduction......Page 256
References......Page 257
1. The conformally invariant (CI) Laplace equation......Page 258
References......Page 259
A.M. Cherubini, G. Metafune & F. Paparella Asymptotic behavior of a bouncing ball......Page 260
References......Page 261
G.M. Coclite & K.H. Karlsen Discontinuous solutions for the Degasperis-Procesi equation......Page 262
References......Page 263
1. Main result......Page 264
References......Page 265
A. Gonzalez-Enriquez & R. de la Llave Analytic approximations of geometric maps and applications to K A M theory......Page 266
References......Page 267
1. The Renormalizatoin group method with Lie symmetry......Page 268
References......Page 269
J. JanySka Utiyama’s reduction method and infinitesimal symmetries of invariant Lagrangians......Page 270
References......Page 271
I.I. Kosenko & S.Ya. Stepanov Stability of the tethered satellite system relative equilibria. Unrestricted problem......Page 272
References......Page 273
E. Maderna & A. Venturelli Globally minimizing parabolic motions in the Newtonian N-body problem......Page 274
References......Page 275
1. Cofactor and bi-cofactor systems......Page 276
2. Families of equivalent flat bi-cofactor systems......Page 277
References......Page 278
L. Martina Symmetry group and symplectic structure for exotic particles in the plane......Page 279
References......Page 281
1. The planar problem......Page 282
References......Page 283
1. Brief description of the results......Page 284
References......Page 285
2. Lax representation......Page 286
References......Page 287
A.R. Rutherford Pseudorotational spectra of molecules and isoparametric geometry......Page 288
References......Page 290
1. Extended abstract......Page 291
References......Page 292
P. van der Kamp Towards global classifications: a diophantine approach......Page 293
References......Page 294
R. Vitolo, H. Broer & C. Sim6 daffeomorphisms The Hopf-saddle-node bifurcation for fixed points of 3D- daffeomorphisms......Page 295
References......Page 296
I. Yehorchenko Relative invariants for Lie algebras: construction and applications......Page 297
References......Page 298
CONFERENCE INFORMATION......Page 300
List of Participants......Page 302
List of Communications......Page 306
Previous SPT Conferences......Page 310