2013/04/05 by Luka Korkut, Korkut, Luka, Domagoj Vlah +3
Mathematics · #28A80 #34C15 #37C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:28A80 #msc:34C15 #msc:37C45
paper · pdf · doi:10.48550/arxiv.1304.1762
new version: some typos corrected, better quality figures arXiv admin note: text overlap with arXiv:1210.6611
arxiv created 2013/07/15 · arxiv updated 2013/07/17
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, and that the corresponding trajectory is a wavy spiral, exhibiting an interesting behavior. The phase dimension of a generalization of the Bessel equation has been also computed.