Potential Analysis

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

Self–similar Energy Forms on the Sierpinski Gasket with Twists

Article

Abstract

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.

Keywords

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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