Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419790 | Applied Mathematics and Computation | 2016 | 15 Pages |
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,xË) in R2 of a solution x=x(t), assuming that (x,xË) 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
Authors
L. Korkut, D. Vlah, V. ŽupanoviÄ,