High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps

Abstract

An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical systems. A quasi-interpolation method due to Hering-Bertram et al. is used to decrease the number of points needed to compute a portion of the manifold. Bézier triangular patches are used in this construction, together with adaptivity conditions based on properties of these patches. Several numerical tests are performed, which show the method to compare favorably with previous approaches.

Jacek Wróbel

Member of Technical Staff, Draper Laboratories

Jacek is a simulation engineer at Draper Labs in Cambridge, MA.

Roy Goodman

Associate Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences

My research interests include dynamical systems and nonlinear waves, vortex dynamics, quantum graphs, and network inference