Miller's instability, microchaos and the short-term evolution of initially nearby orbits

Amina Helmi; Facundo Gomez

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arXiv · 0710.0514

Miller's instability, microchaos and the short-term evolution of initially nearby orbits

Amina Helmi·Facundo Gomez

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Abstract

We study the phase-space behaviour of nearby trajectories in integrable potentials. We show that the separation of nearby orbits initially diverges very fast, mimicking a nearly exponential behaviour, while at late times it grows linearly. This initial exponential phase, known as Miller's instability, is commonly found in N-body simulations, and has been attributed to short-term (microscopic) N-body chaos. However we show here analytically that the initial divergence is simply due to the shape of an orbit in phase-space. This result confirms previous suspicions that this transient phenomenon is not related to an instability in the sense of non-integrable behaviour in the dynamics of N-body systems.

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Amina Helmi, Facundo Gomez. 2007-10-02. Miller's instability, microchaos and the short-term evolution of initially nearby orbits. https://arxiv.org/abs/0710.0514

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