  We review the convergence of chaotic integrals computed by Monte Carlo
simulation, the trace method, dynamical zeta function, and Fredholm determinant
on a simple one-dimensional example: the parabola repeller. There is a dramatic
difference in convergence between these approaches. The convergence of the
Monte Carlo method follows an inverse power law, whereas the trace method and
dynamical zeta function converge exponentially, and the Fredholm determinant
converges faster than any exponential.
