Generalized q-dimension of measures on Heisenberg self-affine sets in the Heisenberg group

Author： Wu Xiaonan   Wu Xiaonan  

Publisher： IOP Publishing

E-ISSN： 1361-6544|28|8|2939-2957

ISSN： 0951-7715

Source： Nonlinearity, Vol.28, Iss.8, 2015-08, pp. : 2939-2957

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Abstract

We study the generalized q-dimension of measures supported by Heisenberg self-affine sets in the Heisenberg group, and we obtain bounds for it which are valid for ‘almost all’ classes of affine contractions. In particular, when 1 < q 2, exact values are established for Heisenberg self-affine measures.

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