Fractal properties of Bessel functions

L. Korkut, D. Vlah and V. Županović

Applied Mathematics and Computation, 2016, vol. 283, issue C, 55-69

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.

Keywords: Wavy spiral; Bessel equation; Generalized Bessel equation; Box dimension; Phase dimension (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:283:y:2016:i:c:p:55-69

DOI: 10.1016/j.amc.2016.02.025

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