Determining the number of integrals of motion by an adapted correlation dimension method.
basic_science · Level V
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- Record sourced from PubMed, PMID 30999503.
- Also identified by DOI 10.1103/PhysRevE.99.032222.
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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.