Floß J, Brumer P. Determining the number of integrals of motion by an adapted correlation dimension method.
Phys Rev E 2019;
99:032222. [PMID:
30999503 DOI:
10.1103/physreve.99.032222]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2018] [Indexed: 11/07/2022]
Abstract
An adapted correlation dimension algorithm is used to numerically determine the number of integrals of motion in a variety of conservative classical systems. The method is demonstrated on three sample systems that display various degrees of integrable and chaotic behavior: the Hénon-Heiles Hamiltonian, an asymmetric top molecule in an electric field, and the planetary system HD128311. Two additional applications of the method emerge: using the adapted correlation dimension algorithm (a) to study partial barriers and turnstiles in phase space and (b) to predict the long-time stability of planetary systems using short-time data.
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