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Analytical solutions of one-dimensional discrete dynamical systems with chaotic behaviour

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Abstract

This paper studies exact analytical solutions in closed form of the difference equation

$$y_{n - 1} = a_k y_n^k + a_{k - 1} y_n^{k - 1} + a_{k - 2} y_n^{k - 2} + \cdot \cdot \cdot + a_p ,$$

when it shows aperiodic ‘chaotic’ behaviour and certain relations amongst the coefficients exist for the solutions to hold. Examples of non-linear difference equations with known analytical solutions are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, King's College, University of London, WC2R 2LS, London, England

    F. Oliveira-Pinto & M. Adibpour

Authors
  1. F. Oliveira-Pinto
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  2. M. Adibpour
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Oliveira-Pinto, F., Adibpour, M. Analytical solutions of one-dimensional discrete dynamical systems with chaotic behaviour. Nonlinear Dyn 1, 121–129 (1990). https://doi.org/10.1007/BF01857783

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  • DOI: https://doi.org/10.1007/BF01857783

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