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Period of the discrete Arnold cat map and general cat map

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Abstract

The paper first studies the period of the discrete Arnold cat map. When the modulo is composite, the formulae are developed to calculate the minimal period. When the modulo is prime, the formulae calculating the period are given and an algorithm is proposed in order to determine the minimal period. Then the paper explores the relationship between the period of the discrete general cat map and its modulo for different parameters a and b. Some period formulae are given and some properties about the period are obtained. In addition, the paper also expands the period formulae of the corresponding a-Fibonacci sequence taken the modulo for more new parameters.

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Acknowledgements

The research is supported by the Fundamental Research Funds for the Central Universities (No. 2011ZM0081) and the National Natural Science Foundation of China (No. 10871074).

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  1. Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510641, P.R. China

    Jianghong Bao & Qigui Yang

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  1. Jianghong Bao
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  2. Qigui Yang
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Correspondence to Jianghong Bao.

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Bao, J., Yang, Q. Period of the discrete Arnold cat map and general cat map. Nonlinear Dyn 70, 1365–1375 (2012). https://doi.org/10.1007/s11071-012-0539-3

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  • DOI: https://doi.org/10.1007/s11071-012-0539-3

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