A superconvergent universality induced by non-associativity |
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Authors: | Chuan-Yun Xu Huan Wang Ke-Fei Cao Shou-Li Peng |
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Institution: | 1. Center for Nonlinear Complex Systems, Department of Physics, School of Physics Science and Technology, Yunnan University, Kunming, Yunnan 650091, China;2. Department of Computer Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721016, China |
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Abstract: | The star products in symbolic dynamics, as effective algebraic operations for describing self-similar bifurcation structure in classical dynamical systems, are found to have either associativity or non-associativity. In this Letter, non-associative star products in trimodal iterative dynamical systems are considered. As the left and right operations have different effects, right-associative star products break the conventional Feigenbaum's metric universality. Through high precision parallel computation, it is found that period-p-tupling bifurcation processes described by right-associative star products exhibit a superconvergent universality of double exponential form. |
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Keywords: | Superconvergent universality Non-associativity Star product Feigenbaum's universality Symbolic dynamics |
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