Transition to stochasticity in Hamiltonian systems: Some numerical results

1 August 1986

journal article
research article
Published by American Physical Society (APS) in Physical Review A

Vol. 34 (2) , 1550-1555
https://doi.org/10.1103/physreva.34.1550

Abstract

We perform numerical experiments on Hamiltonian systems with three degrees of freedom. The correlation dimension, the maximal Lyapunov exponent, and an indicator of the deviation from the harmonic situation are measured. Our results indicate the existence of structures with noninteger correlation dimension at least for finite, but long, observational times. The transition from the motion on the Kolmogorov-Arnol’d-Moser tori to an ergodic motion on the constant-energy surface seems to occur smoothly as energy increases and is difficult to explain in terms of perturbative methods.

Keywords

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