Chongchun Zeng
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.
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