5 papers · 1 filter
On entry-exit formulas for degenerate turning point problems in planar slow-fast systems
Renato Huzak, Kristian Uldall Kristiansen
In this paper, we study degenerate entry-exit problems associated with planar slow-fast systems having an invariant line with a turning point at . The dege…
Fractal analysis of slow-fast and regular systems: A survey of recent results and future perspectives
Renato Huzak, Goran Radunović, Vesna Županović
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit pe…
Ergodicity in planar slow-fast systems through slow relation functions
Renato Huzak, Hildeberto Jardón-Kojakhmetov, Christian Kuehn
In this paper, we study ergodic properties of the slow relation function (or entry-exit function) in planar slow-fast systems. It is well known that zeros of the slow divergence in…
The number of limit cycles for regularized piecewise polynomial systems is unbounded
R. Huzak, K. Uldall Kristiansen
In this paper, we extend the slow divergence-integral from slow-fast systems, due to De Maesschalck, Dumortier and Roussarie, to smooth systems that limit onto piecewise smooth one…
Slow-Fast Torus Knots
Renato Huzak, Hildeberto Jardón-Kojakhmetov
The goal of this paper is to study global dynamics of -smooth slow-fast systems on the -torus of class using geometric singular perturbation theory and the…