Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Posters I
DY 22.50: Poster
Wednesday, March 28, 2012, 17:00–19:00, Poster A
Geometry of inertial manifolds probed via a Lyapunov projection method — •Hong-liu Yang1 and Günter Radons2 — 1Institute of Mechatronic, D-09126 Chemnitz, Germany — 2Chemnitz University of Technology, D-09107 Chemnitz, Germany
A method for determining the dimension and state space geometry of inertial manifolds of dissipative extended dynamical systems is presented. It works by projecting vector differences between reference states and recurrent states onto local linear subspaces spanned by the Lyapunov vectors. A sharp characteristic transition of the projection error occurs as soon as the number of basis vectors is increased beyond the inertial manifold dimension. Since the method can be applied using standard orthogonal Lyapunov vectors, it provides a simple way to determine also experimentally inertial manifolds and their geometric characteristics.