二阶单应差分方程的QRT系统：旋转共轭，周期解的周期，初值敏感性
A QRT-system of two order one homographic difference equations: conjugation to rotations, periods of periodic solutions, sensitiveness to initial conditions
摘要：
研究了单应系统u（n+1）u（n）=c+d/v（n），v（n+1）v（n）=c+d/u（n+1）在正象限内的性质.一个点的轨道包含在一个不变的三次曲线中，并且对相关的动力系统的这个三次曲线的正部分的限制与圆上的旋转共轭。对于初始点的稠密不变集，解是周期的，并且如果c=1（这总是可能的），每个整数n \geq N（d）是某个周期解的最小周期。每个n \geq 11都是某个d>0的解的最小周期，并且我们精确地找到了在2和10之间的这样的最小周期的集合。相应的动力系统在不含不动点的紧集上对初始条件敏感。
英文摘要：
We study the homographic system u(n+1)u(n)=c+d/v(n), v(n+1)v(n)=c+d/u(n+1) in the positive quadrant. The orbit of a point is contained in an invariant cubic curve, and the restriction to the positive part of this cubic of the associated dynamical system is conjugated to a rotation on the circle. For a dense invariant set of initial points the solutions are periodic, and if c=1 (this is always possible) every integer n\geq N(d) is the minimal period of some periodic solution. Every n\geq 11 is the minimal period of some solution for some d>0, and we find exactly the set of such minimal periods between 2 and 10. The associated dynamical system has sensitiveness to initial conditions on every compact set not containing the fixed point.
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