Chaotic complex dynamics and Newton's method |
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| Institution: | 1. University of Illinois, Department of Mathematics, 1409 West Green Street, Urbana, IL 61801, USA;2. University of Illinois, Department of General Engineering, 104 South Mathews Avenue, Urbana, IL 61801, USA;1. Faculty of Science and Technology, Universiti Saina Islam Malaysia (USIM), Malaysia;2. Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Malaysia;3. Institute for Mathematical Research, Universiti Putra Malaysia (UPM), Malaysia;4. Technical Institute of Alsuwerah, The Middle Technical University, Iraq;1. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 340 Xudong Street, Wuhan, 430077, China;2. State Key Laboratory of Geodesy and Earth''s Dynamics, Chinese Academy of Sciences, 340 Xudong Street, Wuhan, 430077, China;3. University of Chinese Academy of Sciences, A19 Yuquan Road, Beijing 100049, China;1. Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, Iran;2. Department of Mathematics, Naragh Branch, Islamic Azad University, Naragh, Iran |
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| Abstract: | We consider one-parameter families of Julia sets arising from Newton's method in the complex domain. We show the existence of bifurcation points where zeros coalesce or change from attractors to repellors, and points where chaotic behavior occurs. |
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