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Vlatko Crnković

Publications and source records attributed to Vlatko Crnković.

2 recordsLinked to original sources
arXiv2025

Fractal Analysis of Pseudo Foci in Piecewise Analytic Systems

It is well known that the Minkowski dimension of spiral trajectories near a non-degenerate focus in analytic (smooth) systems is in one-to-one correspondence with the cyclicity of the focus in generic unfoldings. We give a complete fractal treatment, in terms of the Minkowski dimension and (non-)degeneracy, of spiral trajectories near pseudo foci of piecewise analytic systems. We hope these results will prove useful in the study of bifurcations of such pseudo foci through inherent geometry of associated spiral orbits.

math.DS↗
arXiv2023

Fractal analysis of hyperbolic saddles with applications

In this paper we express the Minkowski dimension of spiral trajectories near hyperbolic saddles and semi-hyperbolic singularities in terms of the Minkowski dimension of intersections of such spirals with transversals near these singularities. We apply these results to hyperbolic saddle-loops and hyperbolic $2$-cycles to obtain upper bounds on the cyclicity of such limit periodic sets.

math.DS↗