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SELF-SIMILAR ENERGIES ON POST-CRITICALLY FINITE SELF-SIMILAR FRACTALS

Published online by Cambridge University Press:  18 August 2006

B. M. HAMBLY ,
V. METZ  and
A. TEPLYAEV
B. M. HAMBLY
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford OX1 3LB, United Kingdomhambly@maths.ox.ac.uk
V. METZ
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford OX1 3LB, United Kingdomhambly@maths.ox.ac.uk
A. TEPLYAEV
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St. Giles', Oxford OX1 3LB, United Kingdomhambly@maths.ox.ac.uk
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Abstract

On a large class of post-critically finite (finitely ramified) self-similar fractals with possibly little symmetry, we consider the question of existence and uniqueness of a Laplace operator. By considering positive refinement weights (local scaling factors) which are not necessarily equal, we show that for each such fractal, under a certain condition, there are corresponding refinement weights which support a unique self-similar Dirichlet form. As compared with previous results, our technique allows us to replace symmetry by connectivity arguments.

Keywords

31C2560J6528A8047H07
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 93 - 112
Copyright
The London Mathematical Society 2006

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