The Periodic Orbits of a Dynamical System Associated with a Family of QRT-Maps

• Bastien, Guy ^[1] ; Rogalski, Marc ^[1]
  1. [1] Sorbonne Université and CNRS
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 2, 2020
• Idioma: inglés
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• Resumen

  • We study the QRT-maps associated with the family of biquadratic curves Cd(K) with equations x2y2-dxy-1+K(x2+y2)=0. With the Prime Number Theorem and the geometry of elliptic cubics we determine the periods of periodic orbits of the dynamical systems defined by these QRT-maps, and prove sensitivity to its initial conditions.