保积的Lozi映射中与抛物周期点和双曲周期点相关的轨道特征
Orbital Characteristics Related to Parabolic and Hyperbolic Periodic Points in Lozi Area-Preserving Map
DOI: 10.12677/APP.2023.1311048, PDF,    科研立项经费支持
作者: 顾恩国, 李 博#：中南民族大学数学与统计学学院，湖北 武汉
关键词: 轨道特征；Lozi保积映射；抛物不动点；双曲不动点；Orbital Characteristics； Lozi Area-Preserving Map； Parabolic Fixed Point； Hyperbolic Fixed Point
摘要: 本文研究了与Lozi保积映射的抛物和双曲周期点相关的轨道特征。证明了其全轨道相对于y=-x都是对称的。首先证明了当a=2时Lozi映射的轨道绕原点旋转，并且指出其轨道可能是发散的，也可能是稳定的周期轨。然后证明了a=-2时Lozi映射的轨道全平面发散，并且发散轨道最终都是属于平行于二四象限的对角平分线的平行直线族。最后证明了当｜a｜＞2时Lozi映射的轨道沿着双曲线在第二或第四象限发散。
Abstract: In this paper, the orbital characteristics associated with a parabolic and hyperbolic periodic point of the Lozi area-preserving map are studied. It is proved that the full trajectory is symmetric about y=-x . We first prove that the trajectory of the Lozi map rotates around the origin, and point out that the trajectory may be divergent or stable periodic when a=2 . Then it is proved that the trajectory of the Lozi map diverges in all planes, and the divergent trajectory eventually belongs to the family of lines parallel to the diagonal bisectors of the two and four quadrants when a=-2 . Finally, it is proved that the trajectory of the Lozi map diverges along the hyperbola in the second or fourth quadrant when ｜a｜＞2 .
文章引用：顾恩国, 李博. 保积的Lozi映射中与抛物周期点和双曲周期点相关的轨道特征[J]. 应用物理, 2023, 13(11): 453-464. https://doi.org/10.12677/APP.2023.1311048

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