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Poincar\'e Recurrences in Microtron and the Global Critical Structure
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The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the exponential transient to exist the two conditions have been shown to be crucial: fast (ballistic) relaxation, and a small measure of the critical structure. The latter was found to include a new peripheral part (halo) of a surprisingly large size. First preliminary empirical evidence is presented for a new regime of Poincar\'e recurrences including the transition from exponential to exponential statistics.
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Massive evaluation and analysis of Poincar\'e recurrences on grids of initial data: a tool to map chaotic diffusion
A grid-based Poincaré recurrence method reproduces Lyapunov stability charts and, via an approximate relation, promises global maps of chaotic diffusion timescales.
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