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Hausdorff and topological dimension for polynomial automorphisms of \mathbb{C}^2

Published online by Cambridge University Press:  06 August 2002

CHRISTIAN WOLF
CHRISTIAN WOLF
Affiliation:
Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisbon, Portugal (e-mail: cwolf@math.ist.utl.pt)
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Abstract

Let g be a polynomial automorphism of \mathbb{C}^2. We study the Hausdorff dimension and topological dimension of the Julia set of g. We show that when g is a hyperbolic mapping, then the Hausdorff dimension of the Julia set is strictly greater than its topological dimension. Moreover, the Julia set cannot be locally connected. We also provide estimates for the dimension of the Julia sets in the general (not necessarily hyperbolic) case.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 4 , August 2002 , pp. 1313 - 1327
Copyright
© 2002 Cambridge University Press

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