Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 16, pp. 1-13.

Title: Persistence of invariant manifolds for
       perturbations of semiflows with symmetry

Author: Chongchun Zeng (Brigham Young Univ., Provo, UT, USA)
         
Abstract: 
Consider a semiflow in a Banach space, which is invariant under the 
action of a compact Lie group. Any equilibrium generates a manifold of 
equilibria under the action of the group. We prove that, if the manifold of 
equilibria is normally hyperbolic, an invariant manifold persists in the 
neighborhood under any small perturbation which may break the symmetry. The 
Liapunov-Perron approach of integral equations is used.     

Submitted in April 1995, revised April 6, 1999, Published May 18, 1999.
Math Subject Classification: 58F15, 58F35, 58G30, 58G35, 34C35.
Key Words:  Semiflow; invariant manifold; symmetry.