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Equivalence among orbital equations of polynomial maps

Author

Listed:
  • Jason A. C. Gallas

    (Instituto de Altos Estudos da Paraíba, Rua Silvino Lopes 419-2502, 58039 190 João Pessoa, Brazil2Complexity Sciences Center, 9225 Collins Ave. 1208, Surfside FL 33154, USA3Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany)

Abstract

This paper shows that orbital equations generated by iteration of polynomial maps do not necessarily have a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear transformations. Five direct and five inverse transformations are established explicitly between a pair of orbits defined by cyclic quintic polynomials with real roots and minimum discriminant. In addition, infinite sequences of transformations generated recursively are introduced and shown to produce unlimited supplies of equivalent orbital equations. Such transformations are generic and valid for arbitrary dynamics governed by algebraic equations of motion.

Suggested Citation

  • Jason A. C. Gallas, 2018. "Equivalence among orbital equations of polynomial maps," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(09), pages 1-11, September.
    • Handle: RePEc:wsi:ijmpcx:v:29:y:2018:i:09:n:s0129183118500821
    DOI: 10.1142/S0129183118500821
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