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Planar self-affine sets with equal Hausdorff, box and affinity dimensions

Published online by Cambridge University Press:  20 October 2016

KENNETH FALCONER  and
TOM KEMPTON
KENNETH FALCONER
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK email [email protected], [email protected]
TOM KEMPTON
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK email [email protected], [email protected]
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Abstract

Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 4 , June 2018 , pp. 1369 - 1388
Copyright
© Cambridge University Press, 2016 

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