Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Mardesic, Pavao"'
Publikováno v:
Phys. D 427 (2021), Paper No. 133017
Let $F\in\mathbb{C}[x,y]$ be a polynomial, $\gamma(z)\in \pi_1(F^{-1}(z))$ a non-trivial cycle in a generic fiber of $F$ and let $\omega$ be a polynomial $1$-form, thus defining a polynomial deformation $dF+\epsilon\omega=0$ of the integrable foliati
Externí odkaz:
http://arxiv.org/abs/2401.05229
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. Here, we expand asymptotically the Lebesgue measure of the epsilon-n
Externí odkaz:
http://arxiv.org/abs/2304.07914
In this paper we study germs of diffeomorphisms in the complex plane. We address the following problem: How to read a diffeomorphism $f$ knowing one of its orbits $\mathbb{A}$? We solve this problem for parabolic germs. This is done by associating to
Externí odkaz:
http://arxiv.org/abs/2112.14324
Publikováno v:
Analysis and Mathematical Physics (2022) 12:114
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 set of poles (i.e. their complex dimensions) and their principal parts w
Externí odkaz:
http://arxiv.org/abs/2010.05955
Autor:
Mardešić, Pavao, Resman, Maja
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 moduli are given by a sequence of Ecalle-Voronin-like germs of analytic dif
Externí odkaz:
http://arxiv.org/abs/1910.06129
Autor:
Mardešić, Pavao, Resman, Maja
Publikováno v:
Ergod. Th. Dynam. Sys. 42 (2022) 195-249
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 (almost regular) germs, that appear as first return maps of hyperbolic
Externí odkaz:
http://arxiv.org/abs/1910.06130
In this paper we study polynomial Hamiltonian systems $dF=0$ in the plane and their small perturbations: $dF+\epsilon\omega=0$. The first nonzero Melnikov function $M_{\mu}=M_{\mu}(F,\gamma,\omega)$ of the Poincar\'e map along a loop $\gamma$ of $dF=
Externí odkaz:
http://arxiv.org/abs/1907.09627
We consider foliations given by deformations $dF+\epsilon\omega$ of exact forms $dF$ in $\mathbb{C}^2$ in a neighborhood of a family of cycles $\gamma(t)\subset F^{-1}(t)$. In 1996 Francoise gave an algorithm for calculating the first nonzero term of
Externí odkaz:
http://arxiv.org/abs/1901.09268
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 asymptotic expansion in the power-iterated log scale.
Comment: 31 pages
Comment: 31 pages
Externí odkaz:
http://arxiv.org/abs/1710.01268
We consider small polynomial deformations of integrable systems of the form $dF=0$, $F\in\mathbb{C}[x,y]$ and the first nonzero term $M_\mu$ of the displacement function $\Delta(t,\epsilon)=\sum_{i=\mu}M_i(t)\epsilon^i$ along a cycle $\gamma(t)\in F^
Externí odkaz:
http://arxiv.org/abs/1703.03837