Baire category and extremely non-normal points of invariant sets ofIFS's

In-Soo Baek; Lars Olsen

doi:10.3934/dcds.2010.27.935

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2010, Volume 27, Issue 3: 935-943. Doi: 10.3934/dcds.2010.27.935

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Baire category and extremely non-normal points of invariant sets of IFS's

In-Soo Baek^1, and
Lars Olsen^2,

1.
Department of Mathematics, Pusan University of Foreign Studies, Pusan 608-738
2.
Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland

Received: August 1, 2009

Revised: December 1, 2009

Published online: March 1, 2010

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Abstract

We prove that if $K$ is the invariant set of an IFS in $\ R^{d}$ satisfying the Strong Open Set Condition, then the set of extremely non-normal points of $K$ is a comeagre subset of $K$.

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Mathematics Subject Classification: Primary: 11K16; Secondary: 28A80.

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