Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Resman, Maja"'
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 intersections of such spirals with transversals near these singularities. We appl
Externí odkaz:
http://arxiv.org/abs/2306.00116
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
A saddle loop is a germ of a holomorphic foliation near a homoclinic saddle connection. We prove that they are classied by their Poincar{\'e} rst-return map. We also prove that they are formally rigid when the Poincar{\'e} map is multivalued. Finally
Externí odkaz:
http://arxiv.org/abs/2112.15058
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
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 complex Dulac germ. The proof uses results about normal forms of hyperbolic
Externí odkaz:
http://arxiv.org/abs/2109.00284
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizi
Externí odkaz:
http://arxiv.org/abs/2105.10660
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 February 2024 530(1)
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