A Method for Generating True Orbits of One-Dimensional Piecewise Linear Fractional Maps and Verification of Its Safety(Application,<Special Topics>Activity Group "Applied Chaos")

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  • Saito Asaki
    Faculty of Systems Information Science, Future University Hakodate

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  • 1次元区分的1次分数写像の真軌道生成法とその安全性検証(応用,<特集>応用カオス研究部会)
  • 1次元区分的1次分数写像の真軌道生成法とその安全性検証
  • 1ジゲン クブンテキ 1ジ ブンスウ シャゾウ ノ シン キドウ セイセイホウ ト ソノ アンゼンセイ ケンショウ

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Abstract

We recently proposed a method for generating true orbits of one-dimensional piecewise linear fractional maps (Physica D, 268 (2014), 100-105). By applying the method to the continued fraction transformation and a modified Bernoulli map, we show that we can obtain true orbits which display the same properties as typical orbits of the two maps. We also conduct verification of Brillhart's cubic irrational that is known to display an unusual occurrence of large partial quotients in its continued fraction expansion, and we report that we can obtain results which support the safety of our true orbit generation method.

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