THE CONVERGENCE OF CHAOTIC INTEGRALS

Details THE CONVERGENCE OF CHAOTIC INTEGRALS THE CONVERGENCE OF CHAOTIC INTEGRALS

1995-05-12

arxiv.org/abs/chao-dyn/9505008v1

Nonlinear Sciences

Chaotic Dynamics

PostScript file with 13 pages, 6 figures in 130372 bytes.

Scientific paper

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.

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