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Postcritical sets and saddle basic sets for Axiom A polynomial skew products on $\mathbb {C}^2$

Published online by Cambridge University Press:  16 May 2012

SHIZUO NAKANE
SHIZUO NAKANE*
Affiliation:
Tokyo Polytechnic University, 1583, Iiyama, Atsugi, Kanagawa 243-0297, Japan (email: nakane@gen.t-kougei.ac.jp)
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Abstract

We investigate the link between postcritical behaviors and the relations of saddle basic sets for Axiom A polynomial skew products on $\mathbb {C}^2$, and characterize various properties concerning the three kinds of accumulation sets defined by DeMarco and Hruska [Axiom A polynomial skew products of $\mathbb {C}^2$ and their postcritical sets. Ergod. Th. & Dynam. Sys.28(2008), 1749–1779] in terms of the saddle basic sets. We also give a new example of higher degree.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 4 , August 2013 , pp. 1124 - 1145
Copyright
Copyright © 2012 Cambridge University Press 

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