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

被引：1

作者：

Bastien, Guy ^{[1
,2
]}

Rogalski, Marc ^{[1
,2
]}

机构：

[1] Sorbonne Univ, IMJ PRG, Paris, France

[2] CNRS, Paris, France

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 02期

关键词：

QRT-maps; Periods q; Dynamical systems;

D O I：

10.1007/s12346-020-00393-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：29

共 22 条

[1]

Appel P, 1897, PRINCIPES THEORIE FO

[2] On the algebraic difference equations un+2un = Ψ(un+1) in R+*, related to a family of elliptic quartics in the plane [J].