Article ID Journal Published Year Pages File Type
6419790 Applied Mathematics and Computation 2016 15 Pages PDF
Abstract

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 R2 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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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