An Asymptotic Comparison of Differentiable Dynamics and Tropical Geometry
An Asymptotic Comparison of Differentiable Dynamics and Tropical Geometry
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DOI：
10.1007/s11040-010-9087-6
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发表时间：
2011-01
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影响因子：
--
通讯作者：
Tsuyoshi Kato
中科院分区：
文献类型：
--
作者：
Tsuyoshi Kato
本文引入了一种新的比较方法，给出了不同演化动力学的粗略渐近估计。它使用一种称为热带几何的尺度变换，将自动机与真实的理性动力学联系起来。通过这个过程，定义方程被变换，而不是解本身。真实的理性动力学被认为是由偏微分方程给出的演化动力学的近似。两种不同的演化动力学可以被认为是当他们的定义方程被转换到同一个自动机在无穷远。
In this paper we introduce a new comparison method to give rough asymptotic estimates of different evolutional dynamics. It uses a kind of scale transform called tropical geometry, which connects automata with real rational dynamics. By this procedure the defining equations are transformed rather than solutions themselves. Real rational dynamics is regarded as an approximation of evolutional dynamics given by partial differential equations (PDEs). Two different evolutional dynamics can be considered when their defining equations are transformed to the same automata at infinity.