  Coupled map lattices of non-hyperbolic local maps arise naturally in many
physical situations described by discretised reaction diffusion equations or
discretised scalar field theories. As a prototype for these types of lattice
dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order
which exhibit strongest possible chaotic behaviour for small coupling constants
a. We prove that the expectations of arbitrary observables scale with \sqrt{a}
in the low-coupling limit, contrasting the hyperbolic case which is known to
scale with a. Moreover we prove that there are log-periodic oscillations of
period \log N^2 modulating the \sqrt{a}-dependence of a given expectation
value. We develop a general 1st order perturbation theory to analytically
calculate the invariant 1-point density, show that the density exhibits
log-periodic oscillations in phase space, and obtain excellent agreement with
numerical results.
