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Some properties of 2-critically finite holomorphic maps of${\bf P}^2$

Published online by Cambridge University Press:  01 February 1998

MATTIAS JONSSON
MATTIAS JONSSON
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden (e-mail: [email protected])
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Abstract

We define 2-critically finite maps of ${\bf P}^2$ and show that they have no nontrivial closed backward invariant sets. In particular, their Julia sets $J_1$, defined as the support of a natural invariant measure, are equal to ${\bf P}^2$. We also prove that repelling periodic points are dense for such maps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 1 , February 1998 , pp. 171 - 187
Copyright
1998 Cambridge University Press

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