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on the relationship between fast lyapunov indicator and periodic orbits for symplectic mappings

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Abstract

The computation on a relatively short time of a quantity, related to the largest Lyapunov Characteristic Exponent, called Fast Lyapunov Indicator allows to discriminate between ordered and weak chaotic motion and also, under certain conditions, between resonant and non resonant regular orbits. The aim of this paper is to study numerically the relationship between the Fast Lyapunov Indicator values and the order of periodic orbits. Using the two-dimensional standard map as a model problem we have found that the Fast Lyapunov Indicator increases as the logarithm of the order of periodic orbits up to a given order. For higher order the Fast Lyapunov Indicator grows linearly with the order of the periodic orbits. We provide a simple model to explain the relationship that we have found between the values of the Fast Lyapunov Indicator, the order of the periodic orbits and also the minimum number of iterations needed to obtain the Fast Lyapunov Indicator values.

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Authors
  1. Elena Lega
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  2. Claude Froeschlé
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Lega, E., Froeschlé, C. on the relationship between fast lyapunov indicator and periodic orbits for symplectic mappings. Celestial Mechanics and Dynamical Astronomy 81, 129–147 (2001). https://doi.org/10.1023/A:1013323507265

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  • DOI: https://doi.org/10.1023/A:1013323507265

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