Normal forms of continuous piecewise linear vector fields and chaotic attractors Part I: Linear vector fields with a section
Normal forms of continuous piecewise linear vector fields and chaotic attractors Part I: Linear vector fields with a section
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连续分段线性向量场和混沌吸引子的正规形式第一部分：具有截面的线性向量场
DOI：
10.1007/bf03167875
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. Komuro
中科院分区：
文献类型：
--
作者：
M. Komuro
本文是一篇由两部分组成的论文的第一部分，它给出了分段线性向量场的范式。在仿射共轭下的混沌吸引子)以及在PL-系统中的原型混沌吸引子。在第一部分中，我们给出了PL-系统的一般形式和在第二部分中起重要作用的具有截面的线性系统的范式。第二部分给出了两区域PL-系统的范式和原型吸引子(螺旋线、双涡卷、双螺杆、螺线、麻雀、Lorenz和Duffing吸引子)，并在第二部分证明了真系统的仿射共轭类由每个区域的特征值唯一地决定。
This paper represents Part I of a 2-part paper which provides the normal forms of piecewise linear vector fields (abbr. PL-systems) under affine conjugacy and the prototype chaotic attractors in the PL-systems. We derive in Part I the general forms of PL-systems and the normal forms of linear systems with a section which play an important role in Part II. The normal forms of 2-region PL-systems and the prototype attractors (Spiral, Double Scroll, Double Screw, Troidal, Sparrow, Lorenz and Duffing attractors) are provided in Part II. It is also proved in Part II that the affine conjugate classes of proper systems are uniquely determined by the eigenvalues in each region.