How many diffusions exist on the Vicsek snowflake?

DOI10.1007/BF01082450zbMath0795.31011MaRDI QIDQ1314876

Volker Metz

Publication date: 14 March 1994

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

diffusionBrownian motionDirichlet formfinitely ramified fractal

Mathematics Subject Classification ID

Dirichlet forms (31C25) Diffusion processes (60J60) Probabilistic potential theory (60J45) Fractals (28A80)

Related Items

EIGENVALUES OF LAPLACIANS ON HIGHER DIMENSIONAL VICSEK SET GRAPHS ⋮ Self-similar energy forms on the Sierpinski gasket with twists ⋮ A grain of dust falling through a Sierpinski gasket ⋮ Uniqueness of eigenforms on fractals - II ⋮ Homogenization of nested fractals ⋮ The cone of diffusions on finitely ramified fractals. ⋮ Existence and uniqueness of diffusions on finitely ramified self-similar fractals ⋮ The ``hot spots conjecture on the Vicsek set ⋮ Uniqueness of eigenforms on fractals ⋮ The short-cut test ⋮ Branching on a Sierpinski graph ⋮ The homogenization problem for Vicsek set ⋮ Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps ⋮ Renormalization contracts on nested fractals. ⋮ Green functions on self-similar graphs and bounds for the spectrum of the Laplacian

Cites Work

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• On time change of symmetric Markov processes
• A diffusion defined on a fractal state space
• Dirichlet forms and analysis on Wiener space
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Brownian motion on nested fractals

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