Abstract
In order to analyze mathematical structures of a transient orbit converging to an equilibrium,
it is of great use to obtain time evolutions of vectors in tangent spaces along the orbit.
We propose a new algorithm to efficiently pull back eigenvectors of linearized system at the equilibrium
by using a modified method to calculate covariant Lyapunov vectors.
These pulled-back vectors are termed pullback vectors in this paper.
We also apply our algorithm to a transient orbit of
a simple three-dimensional ordinary differential equation to give the pullback vectors.
The pullback vectors are used to illustrate appropriate perturbations to give
an orbit whose direction becomes parallel to
the corresponding eigenvector of the linearized system at the equilibrium.
