Apparent fractal dimensions in the HMF model

Abstract

We show that recent observations of fractal dimensions in the $\mu$-space of $N$-body Hamiltonian systems with long-range interactions are due to finite $N$ and finite resolution effects. We provide strong numerical evidence that, in the continuum (Vlasov) limit, a set which initially is not a fractal (e.g. a line in 2D) remains such for all finite times. We perform this analysis for the Hamiltonian Mean Field (HMF) model, which describes the motion of a system of $N$ fully coupled rotors. The analysis can be indirectly confirmed by studying the evolution of a large set of initial points for the Chirikov standard map.

Proceedings of the Vlasovia Workshop, Nancy, 26-28 November 2003. to be published on Transport Theory and Statistical Mechanics (Kluwer)

References in corpus (4)

• Non-Gaussian equilibrium in a long-range Hamiltonian system
• Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
• Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system
• Influence of Expansion on Hierarchical Structure

Cited by in corpus (1)

• Vlasov dynamics of 1D models with long-range interactions