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Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products

Published online by Cambridge University Press:  30 March 2001

HIROKI SUMI
HIROKI SUMI
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1, Oh-okayama, Meguro-ku, Tokyo, 152-8551, Japan (e-mail: sumi@math.titech.ac.jp)
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Abstract

We consider dynamics of sub-hyperbolic and semi-hyperbolic semigroups of rational functions on the Riemann sphere and will show some no wandering domain theorems. The Julia set of a rational semigroup in general may have non-empty interior points. We give a sufficient condition that the Julia set has no interior points. From some information about forward and backward dynamics of the semigroup, we consider when the area of the Julia set is equal to zero or an upper estimate of the Hausdorff dimension of the Julia set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 563 - 603
Copyright
2001 Cambridge University Press

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