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We study the phase-space behaviour of nearby trajectories in integrablepotentials. We show that the separation of nearby orbits initially divergesvery fast, mimicking a nearly exponential behaviour, while at late times itgrows 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 initialdivergence is simply due to the shape of an orbit in phase-space. This resultconfirms previous suspicions that this transient phenomenon is not related toan instability in the sense of non-integrable behaviour in the dynamics ofN-body systems.

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