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The convergence of chaotic integrals
Oliver Bauer1, Ronnie Mainieri
1Theoretical Division, Los Alamos National Laboratory, MS B213, Los Alamos, New Mexico 87545,Center for Nonlinear Studies, Los Alamos National Laboratory, MS B258, Los Alamos, New Mexico 87545,Fachbereich Physik der Universitat Regensburg, Institut II, 93040 Regensburg, Germany.
Abstract:
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. (c) 1997 American Institute of Physics.