Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 16, pp. 1-13.

Persistence of invariant manifolds for perturbations of semiflows with symmetry

Chongchun Zeng

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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Chongchun Zeng
Department of Mathematics
Brigham Young University
Provo, UT 84602, USA
e-mail: zengc@math.byu.edu
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