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Ergodic theory and visualization. II. Harmonic mesochronic plots visualize (quasi)periodic sets

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 نشر من قبل Zoran Levnaji\\'c
 تاريخ النشر 2014
  مجال البحث فيزياء
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We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets or arbitrary periodicity in the phase space. Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision. The range of methods applicability is illustrated using well-known Chirikov standard map, while its full potential is presented by studying higher-dimensional measure-preserving systems, in particular Froeschle map and extended standard map.



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