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Chaos in Two-Dimensional Mappings

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Proceedings of the Second ISAAC Congress

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 8))

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Abstract

In this paper we discuss the existence of chaotic behavior of 2-dimensional mappings. A version of Moser’s theorem is given. As the applications of our discussion, it is proved that the mapping:

$$ \left\{ \begin{array}{l} u = ax + \sum\limits_{k = 1}^n {A_k \sin k(x + y)} \\ v = x + y \\ \end{array} \right. $$

possesses a shift σ of double infinite sequences as a subsystem, if the parameter A k >(1+α)π2/n for k = 1,…,n. This result is an improvement of the known works.

Supported in part by the National Natural Science Foundation of China.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, 100871, P.R. China

    Jian-ying Zhou

Authors
  1. Jian-ying Zhou
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Editor information

Editors and Affiliations

  1. Freie Universität, Berlin, Germany

    Heinrich G. W. Begehr

  2. University of Delaware, Newark, Delaware, USA

    Robert P. Gilbert

  3. Kyushu University, Fukuoka, Japan

    Joji Kajiwara

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© 2000 Kluwer Academic Publishers

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Zhou, Jy. (2000). Chaos in Two-Dimensional Mappings. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0271-1_15

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  • DOI: https://doi.org/10.1007/978-1-4613-0271-1_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7971-3

  • Online ISBN: 978-1-4613-0271-1

  • eBook Packages: Springer Book Archive

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