Comptes Rendus
Complex analysis/Dynamical systems
Brody curves in complicated sets
Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 701-704.

For a hyperbolic generalized Hénon mapping (in the sense of [3]), J+, the boundary of the set of points with bounded orbit is known as a complicated set and also known to admit a lamination by biholomorphic images of C (see [3,6]). We prove that there exists a leaf, which is an injective Brody curve in P2, in the lamination of J+ for certain generalized Hénon mappings (for Brody curves and injective Brody curves, see Subsection 2.2).

L'ensemble J+ des points d'orbite bornée est connu, pour une application de Hénon généralisée hyperbolique (dans le sens de [3]), comme étant un ensemble compliqué admettant une lamination par images biholomorphes de C (voir [3,6]). Nous montrons que, pour certaines applications de Hénon généralisées hyperboliques, une feuille de cette lamination J+ est une courbe de Brody injective dans P2 (voir la sous-section 2.2 pour les notions de courbes de Brody et courbes de Brody injectives).

Published online:
DOI: 10.1016/j.crma.2015.05.001

Taeyong Ahn 1

1 Center for Geometry and its Applications, POSTECH, Pohang 790-784, Republic of Korea
     author = {Taeyong Ahn},
     title = {Brody curves in complicated sets},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {701--704},
     publisher = {Elsevier},
     volume = {353},
     number = {8},
     year = {2015},
     doi = {10.1016/j.crma.2015.05.001},
     language = {en},
AU  - Taeyong Ahn
TI  - Brody curves in complicated sets
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 701
EP  - 704
VL  - 353
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2015.05.001
LA  - en
ID  - CRMATH_2015__353_8_701_0
ER  - 
%0 Journal Article
%A Taeyong Ahn
%T Brody curves in complicated sets
%J Comptes Rendus. Mathématique
%D 2015
%P 701-704
%V 353
%N 8
%I Elsevier
%R 10.1016/j.crma.2015.05.001
%G en
%F CRMATH_2015__353_8_701_0
Taeyong Ahn. Brody curves in complicated sets. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 701-704. doi : 10.1016/j.crma.2015.05.001.

[1] T. Ahn Foliation structure for generalized Hénon mappings, University of Michigan, USA, 2012 (PhD thesis)

[2] T. Ahn Foliation structure for generalized Hénon mappings (preprint) | arXiv

[3] E. Bedford; J. Smillie Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity, Invent. Math., Volume 103 (1991) no. 1, pp. 69-99

[4] E. Bedford; M. Lyubich; J. Smillie Polynomial diffeomorphisms of C2: IV. The measure of maximal entropy and laminar currents, Invent. Math., Volume 112 (1993) no. 1, pp. 77-125

[5] R. Brody Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., Volume 235 (1978), pp. 213-219

[6] J.E. Fornæss; N. Sibony Complex Hénon mappings in C2 and Fatou–Bieberbach domains, Duke Math. J., Volume 65 (1992), pp. 345-380

[7] J.H. Hubbard; R. Oberste-Vorth Hénon mappings in the complex domain I: the global topology of dynamical space, Publ. Math. Inst. Hautes Études Sci., Volume 79 (1994), pp. 5-46

[8] M. Shub Global Stability of Dynamical Systems, Springer-Verlag, 1987

[9] N. Sibony Dynamique des applications rationnelles de Pk, Panor. Synth., Volume 8 (1999), pp. 97-185

Cited by Sources:

Comments - Policy