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A Class of Integrable Non-QRT Mappings and Their Deautonomisation

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Abstract

We study classes of mappings which do not belong to the QRT family. We obtain several integrable non-autonomous forms of these mappings extending previous results where only linearisable cases were found. Using our recently introduced method of singularity confinement with full deautonomisation, we analyse a mapping which, while non-integrable, does possess confined singularities and show that our method makes it possible to obtain the exact value of its algebraic entropy.

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Authors and Affiliations

  1. Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128, Palaiseau, France

    Alfred Ramani

  2. IMNC, Université Paris VII & XI, CNRS, UMR 8165, Bât. 440, 91406, Orsay, France

    Alfred Ramani & Basile Grammaticos

Authors
  1. Alfred Ramani
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  2. Basile Grammaticos
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Correspondence to Basile Grammaticos.

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Ramani, A., Grammaticos, B. A Class of Integrable Non-QRT Mappings and Their Deautonomisation. Lett Math Phys 106, 433–444 (2016). https://doi.org/10.1007/s11005-016-0822-1

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  • DOI: https://doi.org/10.1007/s11005-016-0822-1

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