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Journal Articles Qualitative Theory of Dynamical Systems Year : 2020

THE PERIODIC ORBITS OF A DYNAMICAL SYSTEM ASSOCIATED WITH A FAMILY OF QRT-MAPS

Abstract

We study the QRT-maps associated with the family of biquadratic curves C d (K) with equations x 2 y 2 − dxy − 1 + K(x 2 + y 2) = 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.
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Dates and versions

hal-02884047 , version 1 (29-06-2020)

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Guy Bastien, Marc Rogalski. THE PERIODIC ORBITS OF A DYNAMICAL SYSTEM ASSOCIATED WITH A FAMILY OF QRT-MAPS. Qualitative Theory of Dynamical Systems, 2020, 19 (2), ⟨10.1007/s12346-020-00393-2⟩. ⟨hal-02884047⟩
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