Abstract
A number of new and exciting results on the chaotic properties of dynamical systems have been recently obtained by studying their movable singularities in the complex time plane. New, integrable systems were identified by requiring that their solutions admit only poles. Allowing for logarithmic singularities, it has been possible to distinguish between “strongly” and “weakly” chaotic Hamiltonian systems, while in some cases natural boundaries with self-similar structure have been found. The analysis is direct, widely applicable and is illustrated here on some simple examples.
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