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

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

We study the QRT-maps associated with the family of biquadratic curves C d ( K ) with equations x 2 y 2 - d x y - 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...

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Veröffentlicht in:Qualitative theory of dynamical systems 2020-08, Vol.19 (2), Article 57
Hauptverfasser: Bastien, Guy, Rogalski, Marc
Format: Artikel
Sprache:eng
Schlagworte:
Difference and Functional Equations
Dynamical systems
Dynamical Systems and Ergodic Theory
Initial conditions
Mathematics
Mathematics and Statistics
Orbits
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Zusammenfassung:We study the QRT-maps associated with the family of biquadratic curves C d ( K ) with equations x 2 y 2 - d x y - 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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-020-00393-2