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Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in $ \mathbb{C}^n$


Authors: Tran Vu Khanh and Ninh Van Thu
Journal: Proc. Amer. Math. Soc. 144 (2016), 5197-5206
MSC (2010): Primary 32H50; Secondary 37F99
DOI: https://doi.org/10.1090/proc/13138
Published electronically: May 23, 2016
MathSciNet review: 3556264
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Abstract: Using the lower bounds on the Kobayashi metric established by the first author, we prove a Wolff-Denjoy-type theorem for a very large class of pseudoconvex domains in $ \mathbb{C}^n$. This class includes many pseudoconvex domains of finite type and infinite type.


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Additional Information

Tran Vu Khanh
Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, NSW, Australia, 2522
Email: tkhanh@uow.edu.au

Ninh Van Thu
Affiliation: Department of Mathematics, Vietnam National University at Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
Email: thunv@vnu.edu.vn

DOI: https://doi.org/10.1090/proc/13138
Keywords: Wolff-Denjoy-type theorem, finite type, infinite type, $f$-property, Kobayashi metric, Kobayashi distance
Received by editor(s): July 16, 2015
Received by editor(s) in revised form: December 25, 2015, December 28, 2015, January 13, 2016, and February 4, 2016
Published electronically: May 23, 2016
Additional Notes: The research of the first author was supported by the Australian Research Council DE160100173.
The research of the second author was supported by the Vietnam National University, Hanoi (VNU) under project number QG.16.07. This work was completed when the second author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for the financial support and hospitality.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society