  Weakly chaotic maps with unstable fixed points are investigated in the regime
where the invariant density is non-normalizable. We propose that the infinite
invariant density of these maps can be estimated using as the long time limit
of t^(1-alpha) rho(x, t), in agreement with earlier work of Thaler. Here rho(x,
t) is the normalizable density of particles. This definition uniquely
determines the infinite density and is a valuable tool for numerical
estimations. We use this density to estimate the subexponential separation
lambda_alpha of nearby trajectories. For a particular map introduced by Thaler
we use an analytical expression for the infinite invariant density to calculate
lambda_alpha exactly, which perfectly matches simulations without fitting.
Misunderstanding which recently appeared in the literature is removed.
