Department of Physics and Astronomy: Publications and Other Research


Date of this Version


Document Type



Physical Review E, Volume 48, Number 3, September 1993


Copyright 1993 The American Physical Society


Recent efforts to derive and study a quasiconserved quantity K in the Henon-Heiles problem in terms of a single set of variables are discussed. Numerical results are given, showing how the value of such a quantity varies with time and order in a power-series expansion for K in terms of monomials of the coordinates and velocities. The lowest order in the power series for K corresponds to n =4 and the highest order to n =27, so that 24 orders are included in the series. The results are compared with an earlier study by the authors [Phys. Rev. A 42, 1931 (1990)] that included an expansion for K for orders n =4 to n =15. In general, even in regions where the earlier study suggested that the series for K might be converging, our more recent results [Phys. Rev. A 44, 925 (1991)], involving twice as many orders, suggest that the series diverges.

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