Title: Energy partition on fractals

Authors: Robert S. Strichartz, Jeremy Stanley and Alexander Teplyaev

Issue: Volume 52 (2003), Issue 1, 133-156

Abstract: The energy of a function defined on a post--critically finite self--similar fractal can be written as a sum of directional energies. We show, under mild hypotheses, that each directional energy is a fixed multiple of the total energy, and we compute the multiple for a one-parameter family of energy forms on the Sierpinski gasket. For the standard one, the result is an equipartition of energy principle. Also we discuss the energy partition for general p.c.f. fractals, and the relation of it to the uniqueness and stability of a self-similar Dirichlet form.