Accession Number : ADA185881

Title :   Global Bifurcation of Periodic Solutions with Symmetry,

Corporate Author : BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS

Personal Author(s) : Fiedler, Bernold

PDF Url : ADA185881

Report Date : Jul 1987

Pagination or Media Count : 148

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.

Descriptors :   *BIFURCATION(MATHEMATICS), ALGEBRA, ALGEBRAIC TOPOLOGY, DYNAMICS, GLOBAL, INTERACTIONS, INVARIANCE, MOTION, NUMERICAL ANALYSIS, PERIODIC FUNCTIONS, SOLUTIONS(GENERAL), STATIONARY, SYMMETRY, THEORY, TOPOLOGY

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE