Potential Analysis

, Volume 27, Issue 1, pp 45–60 | Cite as

Self–similar Energy Forms on the Sierpinski Gasket with Twists

  • Mihai Cucuringu
  • Robert S. Strichartz


By introducing twists into the iterated function system that defines the Sierpinski gasket, we are able to construct a unique regular energy form that satisfies a self–similar identity with any prescribed projective weights. Our construction is explicit (involving finding a root of a 4th order polynomial), and we are able to find explicitly a polynomial identity for the algebraic variety containing the smooth manifold of admissible weights. Without the twists, there are obstructions to existence, and a complete description due to Sabot is quite complicated.


Analysis on fractals Self-similar energy forms Sierpinski gasket 

Mathematics Subject Classifications (2000)

28A80 31C45 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentHiram CollegeHiramUSA
  2. 2.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  3. 3.Mathematics Department, Malott HallCornell UniversityIthacaUSA

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