Fractal properties of Bessel functions
Fractal properties of Bessel functions
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贝塞尔函数的分形性质
DOI：
10.1016/j.amc.2016.02.025
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
V. Županović
中科院分区：
文献类型：
--
作者：
Luka Korkut;Domagoj Vlah;V. Županović
利用振动维数和相位维数度量了二阶微分方程解在无穷远点处的分形维数。相维数定义为解x= x（t）在R2中的轨迹（x，xstec）的盒维数，假设（x，xstec）是收敛到原点的螺旋线.本文研究了一类具有振动解的二阶非自治微分方程，包括Bessel方程的相维数。我们证明了Bessel函数的相位维数等于4/3，对于每一阶Bessel函数。轨迹是一个波浪形的螺旋，表现出有趣的振荡行为。还计算了贝塞尔方程的推广的相位维数。
A fractal oscillatority of solutions of second-order differential equations near infinity is measured by oscillatory and phase dimensions. The phase dimension is defined as a box dimension of the trajectory (x, x˙) in R 2 of a solution x= x (t), assuming that (x, x˙) is a spiral converging to the origin. In this work, we study the phase dimension of the class of second-order nonautonomous differential equations with oscillatory solutions including the Bessel equation. We prove that the phase dimension of Bessel functions is equal to 4/3, for each order of the Bessel function. A trajectory is a wavy spiral, exhibiting an interesting oscillatory behavior. The phase dimension of a generalization of the Bessel equation has been also computed.