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 Limit cycles of piecewise linear dynamical systems with three zones and lateral systems Qianqian Zhao,Jiang Yu Keywords:Y-shape systems; Newton-Kantorovich Theorem; limit cycle; lateral systems Abstract: In this paper, we give some evidences what causes more limit cycles for piecewise dynamical systems. We say, the angles or the number of zones are critical points. We study a linear Y-shape system and a linear lateral system, and prove that they has four and five crossing limit cycles by using the Newton-Kantorovich Theorem, respectively.