Global Bifurcation of Periodic Solutions with Symmetry,
Abstract
If we are given a dynamic system with some built-in symmetry, should we except periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? We are lead from dynamics to topology algebra, singularity theory, numerical analysis, and to some applications. A global point of view is one guiding theme along the way: we are mainly interested in periodic motions far from equilibrium. For a method we rely on bifurcation theory, on transversality theory, and on generic approximations. As a reward we encounter known local singularities. As a central new aspect we study the global interaction and interdependence of these local singularities, designing a homotopy invariant. As a result, we obtain an index 'H' which evaluates only information at stationary solutions. Nonzero 'H' implies global Hopf bifurcation of periodic solutions with certain symmetries. Putting it emphatically, 'H' harmonizes symmetry and periodicity. Curiously, 'H' need not be homotopy invariant.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1987
- Accession Number
- ADA185881
Entities
People
- Bernold Fiedler
Organizations
- Brown University