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- W2039766745 abstract "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. Pour mesurer l'oscillarité fractale des solutions àt=∞, nous introduisons les notions de dimension d'oscillarité et de dimension de phase pour les solutions d'une classe d'équations différentielles non linéaires de deuxième ordre. On établit une relation entre ces deux dimensions en utilisant les formules pour box dimension des chirps et pour spirales non rectifiables. Les applications inclusent l'équation de Liénard et oscillateurs faiblement amorties." @default.
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- W2039766745 date "2009-12-01" @default.
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- W2039766745 title "Oscillatory and phase dimensions of solutions of some second-order differential equations" @default.
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- W2039766745 doi "https://doi.org/10.1016/j.bulsci.2008.03.004" @default.
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