The Fatou coordinate for parabolic Dulac germs

被引：8

作者：

Mardesic, P. ^{[1
]}

Resman, M. ^{[2
]}

Rolin, J-P ^{[1
]}

Zupanovic, V ^{[3
]}

机构：

[1] Univ Bourgogne, Inst Math & Bourgogne, Dept Mathemat, BP 47 870, F-21078 Dijon, France

[2] Univ Zagreb, Fac Sci, Dept Math, Bijenicka 30, Zagreb 10000, Croatia

[3] Univ Zagreb, Fac Elect Engn & Comp, Dept Appl Math, Unska 3, Zagreb 10000, Croatia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 266卷 / 06期

关键词：

Dulac germ; Fatou coordinate; Embedding in a flow; Asymptotic expansion; Transseries; EPSILON-NEIGHBORHOODS; NORMAL FORMS; DIFFEOMORPHISMS; CLASSIFICATION; ORBITS;

D O I：

10.1016/j.jde.2018.09.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 logarithm monomials. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：3479 / 3513

页数：35

共 50 条

[1] Analytic moduli for parabolic Dulac germs
Mardesic, P.
Resman, M.
[J]. RUSSIAN MATHEMATICAL SURVEYS, 2021, 76 (03) : 389 - 460
[2] Realization of analytic moduli for parabolic Dulac germs
Mardesic, Pavao
Resman, Maja
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2022, 42 (01) : 195 - 249
[3] ON A QUESTION OF DULAC AND FATOU
MARCO, RP
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 321 (08): : 1045 - 1048
[4] Holomorphic Motions, Fatou Linearization, and Quasiconformal Rigidity for Parabolic Germs
Jiang, Yunping
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2009, 58 (02) : 397 - 414
[5] Linearization of complex hyperbolic Dulac germs
Peran, D.
Resman, M.
Rolin, J. P.
Servi, T.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 508 (01)
[6] A FATOU TYPE THEOREM FOR COMPLEX MAP GERMS
Camara, Leonardo
Scardua, Bruno
[J]. CONFORMAL GEOMETRY AND DYNAMICS, 2012, 16 : 256 - 268
[7] FORMAL POINCARE-DULAC RENORMALIZATION FOR HOLOMORPHIC GERMS
Abate, Marco
Raissy, Jasmin
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (05): : 1773 - 1807
[8] Fatou Flowers and Parabolic Curves
Abate, Marco
[J]. COMPLEX ANALYSIS AND GEOMETRY, KSCV 10, 2015, 144 : 1 - 39
[9] Fatou theorems for parabolic equations
Sweezy, C
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (08) : 2343 - 2355
[10] Fatou Coordinates for Parabolic Dynamics
Ueda, Tetsuo
[J]. COMPLEX GEOMETRY AND DYNAMICS, 2015, : 259 - 270

← 1 2 3 4 5 →