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Massive evaluation and analysis of Poincaré recurrences

Ivan I. Shevchenko; Guillaume Rollin; Alexander V. Melnikov; José Lages


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    <subfield code="a">&lt;p&gt;We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar&amp;eacute; recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. This new method allows one to construct, in some approximation, charts of local diffusion timescales.&lt;/p&gt;</subfield>
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