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Fractal properties of Bessel functions

Author

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  • Korkut, L.
  • Vlah, D.
  • Županović, V.

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.

Suggested Citation

  • Korkut, L. & Vlah, D. & Županović, V., 2016. "Fractal properties of Bessel functions," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 55-69.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:55-69
    DOI: 10.1016/j.amc.2016.02.025
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    Cited by:

    1. Huzak, Renato & Vlah, Domagoj & Žubrinić, Darko & Županović, Vesna, 2023. "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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