Preprint of the project:
12-023 Gary Froyland, Thorsten Hüls, Gary P. Morriss, Thomas M. Watson.
Computing covariant vectors, Lyapunov
vectors, Oseledets vectors and dichotomy projectors: a
comparative numerical study
Covariant vectors, Lyapunov vectors, or
Oseledets vectors are increasingly being used for a variety of
model analyses in areas such as partial differential equations,
nonautonomous differentiable dynamical systems, and random
dynamical systems.
These vectors identify spatially varying directions of specific
asymptotic growth rates and obey equivariance principles. In
recent years new computational methods for approximating
Oseledets vectors have been developed, motivated by increasing
model complexity and greater demands for accuracy. In this
numerical study we introduce two new approaches based on
singular value decomposition and exponential dichotomies and
comparatively review and improve two recent popular approaches
of Ginelli et al. [17] and Wolfe and Samelson [34]. We compare
the performance of the four approaches via three case studies
with very different dynamics in terms of symmetry, spectral
separation, and dimension. We also investigate which methods
perform well with limited data.
