A FATOU TYPE THEOREM FOR COMPLEX MAP GERMS

被引：4
|
作者：
Camara, Leonardo [1 ]
Scardua, Bruno [2 ]
机构：
[1] Univ Fed Espirito Santo, Dept Matemat CCE, CP 68530,Av Fernando Ferrari 514, BR-29075910 Vitoria, ES, Brazil
[2] Univ Fed Rio De Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, RJ, Brazil
来源：
CONFORMAL GEOMETRY AND DYNAMICS | 2012年 / 16卷
关键词：
Complex diffeomorphism germ; parabolic curve; formal separatrix;
D O I：
10.1090/S1088-4173-2012-00242-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove a Fatou type theorem for complex map germs. More precisely, we give (generic) conditions assuring the existence of parabolic curves for complex map germs tangent to the identity, in terms of existence of suitable formal separatrices. Such a map cannot have finite orbits.
引用
收藏
页码：256 / 268
页数：13
相关论文
共 50 条
  • [1] GENERALIZED SPLITTING THEOREM FOR MAP-GERMS
    ICHIKAWA, F
    [J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1983, 59 (09) : 422 - 424
  • [2] Periodic complex map germs and foliations
    Camara, Leonardo M.
    Scardua, Bruno A.
    [J]. ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 2017, 89 (04): : 2563 - 2579
  • [3] A FATOU TYPE THEOREM FOR MULTIPLY SUPERHARMONIC FUNCTIONS
    GowriSankaran, Kohur
    [J]. POTENTIAL THEORY AND STOCHASTICS IN ALBAC: AUREL CORNEA MEMORIAL VOLUME, CONFERENCE PROCEEDINGS, 2009, : 139 - 144
  • [4] Finiteness theorem for topological contact equivalence of map germs
    Birbrair, Lev
    Ferreira Costa, Joao Carlos
    Fernandes, Alexandre
    [J]. HOKKAIDO MATHEMATICAL JOURNAL, 2009, 38 (03) : 511 - 517
  • [5] The Fatou coordinate for parabolic Dulac germs
    Mardesic, P.
    Resman, M.
    Rolin, J-P
    Zupanovic, V
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (06) : 3479 - 3513
  • [6] A Livsic type theorem for germs of analytic diffeomorphisms
    Navas, Andres
    Ponce, Mario
    [J]. NONLINEARITY, 2013, 26 (01) : 297 - 305
  • [7] A GENERALIZED FATOU THEOREM
    MAIR, BA
    SINGMAN, D
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 300 (02) : 705 - 719
  • [8] On Fatou’s theorem
    Arthur A. Danielyan
    [J]. Analysis and Mathematical Physics, 2020, 10
  • [9] On Fatou's theorem
    Danielyan, Arthur A.
    [J]. ANALYSIS AND MATHEMATICAL PHYSICS, 2020, 10 (03)
  • [10] A RELATIVIZED FATOU THEOREM
    DOOB, JL
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1959, 45 (02) : 215 - 222
12345