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- W4301394627 abstract "• Box dimension of degenerate spiral trajectory. • 2-dimensional spiral with different asymptotic. • 3-dimensional spiral with different asymptotic. • Numerical computation of the box dimension. In this paper we initiate the study of the Minkowski dimension, also called the box dimension, of degenerate spiral trajectories of a class of ordinary differential equations. A class of singularities of focus type with two zero eigenvalues (nilpotent or more degenerate) has been studied. We find the box dimension of a polynomial degenerate focus of type ( n , n ) by exploiting the well-known fractal results for α -power spirals. In the general ( m , n ) case, we formulate a conjecture about the box dimension of a degenerate focus using numerical experiments. Further, we reduce the fractal analysis of planar nilpotent contact points to the study of the box dimension of a slow-fast spiral generated by their “entry-exit” function. There exists a bijective correspondence between the box dimension of the slow-fast spirals and the codimension of contact points. We also construct a three-dimensional vector field that contains a degenerate spiral, called an elliptical power spiral, as a trajectory." @default.
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- W4301394627 date "2023-02-01" @default.
- W4301394627 modified "2023-09-24" @default.
- W4301394627 title "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations" @default.
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- W4301394627 doi "https://doi.org/10.1016/j.amc.2022.127569" @default.
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