| Institution: | School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0190 - Department of Mathematics, National University of Singapore, Singapore 119262 ; Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211 ; School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0190 |
| Abstract: | We study dynamics of flows generated by smooth vector fields in  in the vicinity of an invariant and closed smooth manifold  . By applying the Hadamard graph transform technique, we show that there exists an invariant manifold (called a center manifold of  ) based on the information of the linearization along  , which contains every locally bounded solution and is persistent under small perturbations. |
