18 citations · 34 across the 7 of their papers we have counts for
6 papers · 1 filter
The Fatou coordinate for parabolic Dulac germs
Pavao Mardesic, Maja Resman, Jean-Philippe Rolin +1
We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asympt…
A note on the box dimension of degenerate foci
Domagoj Vlah, Darko Zubrinic, Vesna Zupanovic
We study polynomial planar systems with singularity of focus type without characteristic directions. Simple and natural transformation of weak focus has been used to obtain such de…
Formal normal forms and formal embeddings into flows for power-log transseries
Pavao Mardesic, Maja Resman, Jean-Philippe Rolin +1
The Dulac series are the asymptotic expansions of first return maps in a neighborhood of a hyperbolic polycycle. In this article, we consider two algebras and of power-log transser…
Fractal analysis of Hopf bifurcation at infinity
Goran Radunović, Vesna Županović, Darko Žubrinić
Using geometric inversion with respect to the origin we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent defi…
Box dimension of unit-time map near nilpotent singularity of planar vector field
Lana Horvat Dmitrovic, Vesna Zupanovic
The connection between discrete and continuous dynamical systems through the unit-time map has shown a significant role in bifurcation theory. Recently, it has also been used in fr…
Multiplicity of fixed points and growth of epsilon-neighbourhoods of orbits
Pavao Mardesic, Maja Resman, Vesna Zupanovic
We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on epsilon of the length of epsilon-neighborhood of any orbit of g, tending…