Equivalence among orbital equations of polynomial maps

Jason A. C. Gallas
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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

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 09, 1-11

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.

Keywords: Quadratic map; symbolic computation; algebraic structures; algebraic methods (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0129183118500821

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