THE CONVERGENCE OF CHAOTIC INTEGRALS

We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm d eterminant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approache s. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exp onentially, and the Fredholm determinant converges faster than any exp onential. (C) 1997 American Institute of Physics.