Charles Karney: Publication 30/85, Rechester(1983)

A. B. Rechester, M. N. Rosenbluth, R. B. White, and C. F. F. Karney.
Statistical description of the Chirikov-Taylor model in the presence of noise.
In C. W. Horton, L. E. Reichl, and V. G. Szebehely, editors, Long-Time Prediction in Dynamics, volume II of Wiley-Interscience Series on Nonequilibrium Problems in the Physical Sciences and Biology, pages 471–483, Wiley, New York, 1983.
Preprint lakeway.
Proc. Workshop on Long-Time Predictions in Nonlinear Conservative Dynamical Systems, Lakeway, TX, Mar. 16–19, 1981.
Reprint: ltpd83
BibTeX Entry

A review of recent analytical and numerical results concerning the Chirikov-Taylor model is given. It is shown that the presence of noise makes the statistical description of this system unique. The form of the diffusion coefficient is quite different depending on the nature of the dynamical orbits (integrable, stochastic, or accelerator). We have found that in the presence of noise, dynamical averaging, performed numerically, and statistical averaging, performed analytically with the path-integral method, are the same. Some unsolved problems are presented and discussed.