Ebook: Dynamics, Bifurcation and Symmetry: New Trends and New Tools

This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci­ entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic­ ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam­ ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc­ cess of this conference.

---

---

Content:
Front Matter....Pages i-xv
A Spatial Center Manifold Approach to a Hydrodynamical Problem with O(2) Symmetry....Pages 1-10
Analyzing Bifurcations in the Kolmogorov Flow Equations....Pages 11-33
Oscillator Networks with the Symmetry of the Unit Quaternion Group....Pages 35-48
An Investigation of a Mode Interaction Involving Period-Doubling and Symmetry-Breaking Bifurcations....Pages 49-58
Sets, Lines and Adding Machines....Pages 59-68
Mixed-Mode Solutions in Mode Interaction Problems with Symmetry....Pages 69-77
A Classification of 2-Modes Interactions with SO(3) Symmetry and Applications....Pages 79-95
Non Linear Parabolic Evolutions in Unbounded Domains....Pages 97-104
Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom....Pages 105-110
Blowing-Up in Equivariant Bifurcation Theory....Pages 111-122
A Remark on the Detection of Symmetry of Attractors....Pages 123-125
Coupled Cells: Wreath Products and Direct Products....Pages 127-138
Hopf Bifurcations on Generalized Rectangles with Neumann Boundary Conditions....Pages 139-158
The Role of Geometry in Computational Dynamics....Pages 159-165
Hopf Bifurcation at k-Fold Resonances in Equivariant Reversible Systems*....Pages 167-179
Symmetries and Reversing Symmetries in Kicked Systems....Pages 181-196
Exclusion of Relative Equilibria....Pages 197-203
Bifurcation of Periodic Orbits in 1:2 Resonance: A Singularity Theory Approach....Pages 205-219
Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance....Pages 221-240
Instantaneous Symmetry and Symmetry on Average in the Couette-Taylor and Faraday Experiments....Pages 241-257
The Path Formulation of Bifurcation Theory....Pages 259-278
Codimension Two Local Analysis of Spherical B?nard Convection....Pages 279-289
A Geometric Hamiltonian Approach to the Affine Rigid Body....Pages 291-299
A Note on Discontinuous Vector Fields and Reversible Mappings....Pages 301-310
Bifurcation of Singularities Near Reversible Systems....Pages 311-325
On a New Phenomenon in Bifurcations of Periodic Orbits....Pages 327-331
An Inhomogeneous Picard-Fuchs Equation....Pages 333-341
Hopf Bifurcation in Symmetrically Coupled Lasers....Pages 343-354

---

Content:
Front Matter....Pages i-xv
A Spatial Center Manifold Approach to a Hydrodynamical Problem with O(2) Symmetry....Pages 1-10
Analyzing Bifurcations in the Kolmogorov Flow Equations....Pages 11-33
Oscillator Networks with the Symmetry of the Unit Quaternion Group....Pages 35-48
An Investigation of a Mode Interaction Involving Period-Doubling and Symmetry-Breaking Bifurcations....Pages 49-58
Sets, Lines and Adding Machines....Pages 59-68
Mixed-Mode Solutions in Mode Interaction Problems with Symmetry....Pages 69-77
A Classification of 2-Modes Interactions with SO(3) Symmetry and Applications....Pages 79-95
Non Linear Parabolic Evolutions in Unbounded Domains....Pages 97-104
Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom....Pages 105-110
Blowing-Up in Equivariant Bifurcation Theory....Pages 111-122
A Remark on the Detection of Symmetry of Attractors....Pages 123-125
Coupled Cells: Wreath Products and Direct Products....Pages 127-138
Hopf Bifurcations on Generalized Rectangles with Neumann Boundary Conditions....Pages 139-158
The Role of Geometry in Computational Dynamics....Pages 159-165
Hopf Bifurcation at k-Fold Resonances in Equivariant Reversible Systems*....Pages 167-179
Symmetries and Reversing Symmetries in Kicked Systems....Pages 181-196
Exclusion of Relative Equilibria....Pages 197-203
Bifurcation of Periodic Orbits in 1:2 Resonance: A Singularity Theory Approach....Pages 205-219
Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance....Pages 221-240
Instantaneous Symmetry and Symmetry on Average in the Couette-Taylor and Faraday Experiments....Pages 241-257
The Path Formulation of Bifurcation Theory....Pages 259-278
Codimension Two Local Analysis of Spherical B?nard Convection....Pages 279-289
A Geometric Hamiltonian Approach to the Affine Rigid Body....Pages 291-299
A Note on Discontinuous Vector Fields and Reversible Mappings....Pages 301-310
Bifurcation of Singularities Near Reversible Systems....Pages 311-325
On a New Phenomenon in Bifurcations of Periodic Orbits....Pages 327-331
An Inhomogeneous Picard-Fuchs Equation....Pages 333-341
Hopf Bifurcation in Symmetrically Coupled Lasers....Pages 343-354
....