26 citations · 128 across the 22 of their papers we have counts for
15 papers · 1 filter
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…
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…
Infinitesimal Center Problem on zero cycles and the composition conjecture
A. Álvarez, J. L. Bravo, C. Christopher +1
We study the analogue of the classical infinitesimal center problem in the plane, but for zero cycles. We define the displacement function in this context and prove that it is iden…
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…
Infinite Orbit depth and length of Melnikov functions
Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1
In this paper we study polynomial Hamiltonian systems in the plane and their small perturbations: . The first nonzero Melnikov function of the Poin…
Godbillon-Vey sequence and Francoise algorithm
Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla +1
We consider foliations given by deformations of exact forms in in a neighborhood of a family of cycles . In 1996 Francoise gave a…
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…
Length of epsilon-neighborhoods of orbits of Dulac maps
P. Mardesic, M. Resman, J. -P. Rolin +1
By Dulac maps we mean first return maps of hyperbolic polycycles of analytic planar vector fields. We study the fractal properties of the orbits of a parabolic Dulac map. To this e…
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…
Index of Singularities of Real Vector Fields on Singular Hypersurfaces
Pavao Mardesic
Gómez-Mont, Seade and Verjovsky introduced an index, now called GSV-index, generalizing the Poincaré-Hopf index to complex vector fields tangent to singular hypersurfaces. The GSV-…
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…
Vanishing Abelian integrals on zero-dimensional cycles
Amelia Álvarez Sánchez, José Luis Bravo Trinidad, Pavao Mardesić
In this paper we study conditions for the vanishing of Abelian integrals on families of zero-dimensional cycles. That is, for any rational function , characterize all rationa…
Pseudo-Abelian integrals on slow-fast Darboux systems
Marcin Bobienski, Pavao Mardesic, Dmitry Novikov
We study pseudo-Abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number o…
Pseudo-Abelian integrals: unfolding generic exponential case
Marcin Bobienski, Pavao Mardesic, Dmitry Novikov
We consider an integrable polynomial system with generalized Darboux first integral H_0. We assume that it defines a family of real cycles in a region bounded by a polycycle. To an…