  We explore the high dimensional chaos of a one-dimensional lattice of
diffusively coupled tent maps using the covariant Lyapunov vectors (CLVs). We
investigate the connection between the dynamics of the maps in the physical
space and the dynamics of the covariant Lyapunov vectors and covariant Lyapunov
exponents that describe the direction and growth (or decay) of small
perturbations in the tangent space. We explore the tangent space splitting into
physical and transient modes and find that the splitting persists for all of
the conditions we explore. In general, the leading CLVs are highly localized in
space and the CLVs become more delocalized with increasing Lyapunov index. We
consider the dynamics with a conservation law whose strength is controlled by a
parameter that can be continuously varied. Our results indicate that a
conservation law delocalizes the spatial variation of the CLVs. We find that
when a conservation law is present, the leading CLVs are entangled with fewer
of their neighboring CLVs than in the absence of a conservation law.
