TY - JOUR
T1 - Dynamics of Polynomial Diffeomorphisms of C2
T2 - Combinatorial and Topological Aspects
AU - Ishii, Yutaka
N1 - Funding Information:
Acknowledgements The author thanks Laurent Bartholdi, Eric Bedford, Romain Dujardin, John Hubbard, Hiroyuki Inou, Sarah Koch, Mitsuhiro Shishikura, John Smillie and Shigehiro Ushiki for their comments on the subjects of the manuscript. He is also grateful to the anonymous referee for his/her careful reading of the manuscript and detailed comments. This research is partially supported by JSPS KAKENHI Grant Numbers 25287020 and 25610020.
Publisher Copyright:
© 2017, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - The Fig. 1 was drawn by Shigehiro Ushiki using his software called HenonExplorer. This complicated object is the Julia set of a complex Hénon map fc , b(x, y) = (x2+ c- by, x) defined on C2 together with its stable and unstable manifolds, hence it is a fractal set in the real 4-dimensional space! The purpose of this paper is to survey some results, questions and problems on the dynamics of polynomial diffeomorphisms of C2 including complex Hénon maps with an emphasis on the combinatorial and topological aspects of their Julia sets.
AB - The Fig. 1 was drawn by Shigehiro Ushiki using his software called HenonExplorer. This complicated object is the Julia set of a complex Hénon map fc , b(x, y) = (x2+ c- by, x) defined on C2 together with its stable and unstable manifolds, hence it is a fractal set in the real 4-dimensional space! The purpose of this paper is to survey some results, questions and problems on the dynamics of polynomial diffeomorphisms of C2 including complex Hénon maps with an emphasis on the combinatorial and topological aspects of their Julia sets.
UR - http://www.scopus.com/inward/record.url?scp=85034656043&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85034656043&partnerID=8YFLogxK
U2 - 10.1007/s40598-017-0066-x
DO - 10.1007/s40598-017-0066-x
M3 - Article
AN - SCOPUS:85034656043
VL - 3
SP - 119
EP - 173
JO - Arnold Mathematical Journal
JF - Arnold Mathematical Journal
SN - 2199-6792
IS - 1
ER -