Smooth potential chaos and N-body simulations

Abstract

Integrations in fixed N-body realisations of smooth density distributions corresponding to a chaotic galactic potential can be used to derive reliable estimates of the largest (finite time) Lyapunov exponent X_S associated with an orbit in the smooth potential generated from the same initial condition, even though the N-body orbit is typically characterised by an N-body exponent X_N >> X_S. This can be accomplished either by comparing initially nearby orbits in a single N-body system or by tracking orbits with the same initial condition evolved in two different N-body realisations of the same smooth density.

9 pages plus 7 figures, expanded version to appear in Astrophysical Journal

References in corpus (4)

• Instability of the Gravitational N-Body Problem in the Large-N Limit
• Chaos and the continuum limit in the gravitational N-body problem. I. Integrable potentials
• Chaos and the continuum limit in the gravitational N-body problem II. Nonintegrable potentials
• Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems

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• Probing the shape and history of the Milky Way halo with orbital spectral analysis
• Chaos and chaotic phase mixing in cuspy triaxial potentials
• On relaxation processes in collisionless mergers
• On the relevance of chaos for halo stars in the solar neighbourhood II
• The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation
• Henry Kandrup's Ideas About Relaxation of Stellar Systems
• Appropriate SCF basis sets for orbital studies of galaxies and a `quantum-mechanical' method to compute them
• $N$-body chaos and the continuum limit in numerical simulations of self-gravitating systems, revisited
• Hierarchical generative models for star clusters from hydro-dynamical simulations
• Chaotic mixing and the secular evolution of triaxial cuspy galaxy models built with Schwarzschild's method
• Errors, chaos and the collisionless limit
• $N$-body chaos, phase-space transport and relaxation in numerical simulations
• On time-dependent orbital complexity in gravitational N-body simulations
• Chaos in violent relaxation dynamics. Disentangling micro- and macro-chaos in numerical experiments of dissipationless collapse