螺线管管壁构造法及其混沌特性计算机证明

Construction Method of Pipe Wall of Solenoid and Computer Proof of Solenoid Chaotic Properties

提出螺线管“管壁构造法”，构造映射ｆ（θ，ｐ）＝（２θ，ａｐ＋ｅｉθ）在实心环面Ｄ中具有“强收缩和圆周倍扩张”的可变维数的螺线管吸引子．提出了Ｄ中任意断面（θ，Ｂ２θ）中心点在ｆｎ作用下的表达式．构造了在ｆｎ作用下任意断面的三维及二维断面图．提出不同维数（不同断面压缩比ａ）的螺线管吸引子的稠密周期点计算公式．用计算机证明了螺线管吸引子的敏感、稠密周期点、拓扑传递这三个混沌特性．分析了ｆ吸引子的分形维数．

According to the ' construction method of pipe wall of solenoid ',constructs the solenoid attractor under the mapping f(θ,p)=(2θ,ap+ e i θ ) in the solid torus D ,which is dimension changeable and squeezed in cross section and stretched twice along circumference. The representation of the center point of any cross section after iterating f n is brought up. The 3 D and 2 D images of any cross section under the action of f n are generated. We develop the computing formula of dense period point of solenoid attractor with different dimensions (different squeezing ratio a ). Three chaotic charaters of the attractor,which are verified by computor, are sensitivity,dense period point and topological transferability.