18 citations · 34 across the 7 of their papers we have counts for
10 papers
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…
Oscillatory Integrals and Fractal Dimension
Jean-Philippe Rolin, Domagoj Vlah, Vesna Zupanovic
We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude with compact support. Geometrical properties of the curves defin…
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…
Fractal properties of Bessel functions
Luka Korkut, Domagoj Vlah, Vesna Zupanovic
A fractal oscillatority of solutions of second-order differential equations near infinity is measured by oscillatory and phase dimensions. The phase dimension is defined as a box d…
Geometrical properties of a class of systems with spiral trajectories in R^3
Luka Korkut, Domagoj Vlah, Vesna Zupanovic
Here we study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the point of view of fractal geometry. The fracta…
Wavy spirals and their fractal connection with chirps
Luka Korkut, Domagoj Vlah, Darko Zubrinic +1
We study the fractal oscillatority of a class of real functions near . It is measured by oscillatory and phase dimensions, defined as box dimensions of the…
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…