Abstract
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.
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Komuro, M. Normal forms of continuous piecewise linear vector fields and chaotic attractors Part I: Linear vector fields with a section. Japan J. Appl. Math. 5, 257–304 (1988). https://doi.org/10.1007/BF03167875
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DOI: https://doi.org/10.1007/BF03167875