Automata in Groups and Dynamics and Induced Systems of PDE in Tropical Geometry

被引：0
作者：
Tsuyoshi Kato
机构：
[1] Kyoto University,Department of Mathematics, Faculty of Science
来源：
The Journal of Geometric Analysis | 2014年 / 24卷
关键词：
Automata groups; Tropical geometry; Dynamical scale transform; Asymptotic comparison of PDE; 35A30; 39A22; 20E08; 14T99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we develop a dynamical scaling limit from rational dynamics to automata in tropical geometry. We compare these dynamics and induce uniform estimates of their orbits. We apply these estimates to introduce a comparison analysis of theory of automata groups in geometric group theory with analysis of rational dynamics and some hyperbolic PDE systems. Frameworks of characteristic properties of automata groups are inherited to the corresponding rational or PDE dynamics. As an application we study the Burnside problem in group theory and translate the property as the infinite quasi-recursiveness in rational dynamics.
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页码：901 / 987
页数：86
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