2012/10/24 by Luka Korkut, Korkut, Luka, Domagoj Vlah +7 · 1 citation
Mathematics · #28A80 #34C15 #37C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Morphological variations and asymmetry #math.CA #msc:28A80 #msc:34C15 #msc:37C45
paper · pdf · doi:10.48550/arxiv.1210.6611
openalex publication_date 2012/10/24 · arxiv created 2014/04/21 · arxiv updated 2014/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the fractal oscillatority of a class of real C1 functions x=x(t) near t=∞. It is measured by oscillatory and phase dimensions, defined as box dimensions of the graph of X(τ)=x(\frac1τ) near τ=0 and the trajectory (x,x) in ℝ2, respectively, assuming that (x,x) is a spiral converging to the origin. The relationship between these two dimensions has been established for a class of oscillatory functions using formulas for box dimensions of graphs of chirps and nonrectifiable wavy spirals, introduced in this paper. Wavy spirals are a specific type of spirals, given in polar coordinates by r=f(φ), converging to the origin in non-monotone way as a function of φ. They emerged in our study of phase portraits associated to solutions of Bessel equations. Also, the rectifiable chirps and spirals have been studied.