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Oscillatory and phase dimensions of solutions of some second-order differential equations

In order to measure fractal oscillatority of solutions at $\infty$, 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 Lienard equation and weakly damped oscillators.

nonlinear differential equation; nonlinear oscillations; box dimension; chirp; spiral; Lienard equation; weakly damped oscillator

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