18 citations · 49 across the 13 of their papers we have counts for
17 papers
Fractal analysis of hyperbolic saddles with applications
Vlatko Crnković, Renato Huzak, Maja Resman
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 intersectio…
Reading multiplicity in unfoldings from epsilon-neighborhoods of orbits
Renato Huzak, Pavao Mardešić, Maja Resman +1
We consider generic 1-parameter unfoldings of parabolic vector fields. It is known that the box dimension of orbits of their time-one maps is discontinuous at the bifurcation value…
Rigidity of saddle loops
Daniel Panazzolo, Maja Resman, Loïc Teyssier
A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classied by their Poincar{é} rst-return map. We also prove that they…
Reading analytic invariants of parabolic diffeomorphisms from their orbits
Martin Klimes, Pavao Mardesic, Goran Radunovic +1
In this paper we study germs of diffeomorphisms in the complex plane. We address the following problem: How to read a diffeomorphism knowing one of its orbits ? We…
Linearization of complex hyperbolic Dulac germs
Dino Peran, Maja Resman, Jean-Philippe Rolin +1
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a compl…
Normal forms of hyperbolic logarithmic transseries
Dino Peran, Maja Resman, Jean-Philippe Rolin +1
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient conditi…
Fractal zeta functions of orbits of parabolic diffeomorphisms
Pavao Mardešić, Goran Radunović, Maja Resman
In this paper, we prove that fractal zeta functions of orbits of parabolic germs of diffeomorphisms can be meromorphically extended to the whole complex plane. We describe their se…
Realization of analytic moduli for parabolic Dulac germs
Pavao Mardešić, Maja Resman
In a previous paper we have determined analytic invariants, that is, moduli of analytic classification, for parabolic generalized Dulac germs. This class contains parabolic Dulac (…
Analytic moduli for parabolic Dulac germs
Pavao Mardešić, Maja Resman
In this paper we give moduli of analytic classification for parabolic Dulac i.e. almost regular germs. Dulac germs appear as first return maps of hyperbolic polycycles. Their modul…
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…
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…
Box dimension of a hyperbolic saddle loop
Maja Resman
We compute the box dimension of a spiral trajectory around a hyperbolic saddle loop, as the simplest example of a hyperbolic saddle polycycle. In cases of weak foci and limit cycle…
Fixed points of diffeomorphisms, singularities of vector fields and epsilon-neighborhoods of their orbits, the thesis
Maja Resman
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a…
Epsilon-neighborhoods of orbits of parabolic diffeomorphisms and cohomological equations
Maja Resman
In this article, we study analyticity properties of (directed) areas of epsilon-neighborhoods of orbits of parabolic germs. The article is motivated by the question of analytic cla…
Invariance of the normalized Minkowski content with respect to the ambient space
Maja Resman
It is easy to show that the lower and the upper box dimensions of a bounded set in Euclidean space are invariant with respect to the ambient space. In this article we show that the…
Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms
Maja Resman
In this article we study the dynamics generated by germs of parabolic diffeomorphisms f : (C; 0)->(C; 0) tangent to the identity. We show how formal classification of a given parab…
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…