Oscillatory and phase dimensions of solutions of some second-order differential equations
Oscillatory and phase dimensions of solutions of some second-order differential equations
复制标题
一些二阶微分方程解的振荡维数和相位维数
DOI：
10.1016/j.bulsci.2008.03.004
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发表时间：
2009
影响因子：
1.3
通讯作者：
V. Županović
中科院分区：
文献类型：
--
作者：
Mervan Pašić;D. Zubrinic;V. Županović
为了测量t=∞处解的分形振荡性，我们定义了一类二阶非线性微分方程解的振荡维数和相维数。利用啁啾和不可整流螺旋的盒维计算公式，得到了这两个维度之间的关系。应用包括lisamadard方程和弱阻尼振荡器。
In order to measure fractal oscillatority of solutions at t=∞, we define oscillatory and phase dimensions of solutions of a class of second-order nonlinear differential equations. The relation between these two dimensions is found using formulas for box dimension of chirps and nonrectifiable spirals. Applications include the Liénard equation and weakly damped oscillators.