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Self-Similar Energies on Finitely Ramified Fractals
Hardcover
Series: Fractals & Dynamics in Math, Science, & the Arts
ISBN13: 9789819809141
Publisher: World Scientific Publishing Company
Published: Nov 4 2025
Pages: 492
Weight: 1.81
Height: 1.06 Width: 6.00 Depth: 9.00
Language: English
This monograph delves into the theory of self-similar energies on finitely ramified self-similar fractals. Using these self-similar energies, one can construct Laplacians, harmonic functions, Brownian motion, and differential equations specific to these fractals.
On finitely ramified fractals, self-similar energies are derived from eigenforms - quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores conditions for the existence and uniqueness of these self-similar energies and addresses related problems. For certain cases, complete solutions are provided.
Analysis on fractals began to take shape as a mathematical field in the late 1980s. Traditionally, the focus of analysis has been on finitely ramified fractals - those in which copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive.
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