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

**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.

Show me the
PDF file (154K),
TEX file, and other files for this article.

Chongchun Zeng

Department of Mathematics

Brigham Young University

Provo, UT 84602, USA

e-mail: zengc@math.byu.edu

Return to the EJDE web page