Abstract
We consider Kusuoka's construction of Dirichlet forms on the Vicsek snowflake. a nested fractal. His method is generalized and all irreducible, local Dirichlet forms which can be constructed in this way are characterized. We end up with a one-parameter family of different possible forms. This proves that ‘Brownian motion’ on fractals is not unique if the isometry group of the fractal is too small.
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Metz, V. How many diffusions exist on the Vicsek snowflake?. Acta Appl Math 32, 227–241 (1993). https://doi.org/10.1007/BF01082450
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DOI: https://doi.org/10.1007/BF01082450