Numerical study of a high-order quasiconserved quantity in the Henon-Heiles problem

Authors

• Paul Finkler, University of Nebraska-LincolnFollow
• C. Edward Jones, University of Nebraska-Lincoln
• Glenn A. Sowell, University of Nebraska at Omaha

Document Type

Article

Date of this Version

9-1993

Citation

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

Comments

Copyright 1993 The American Physical Society

Abstract

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.