Self-similar Energies On Finitely Ramified Fractals
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A01=Roberto Peirone
Analysis on Fractals
Author_Roberto Peirone
Brownian Motion
Category=PBKF
Category=PBMX
Differential Equations
Dirichlet Forms
Eigenforms
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Finitely Ramified Self-Similar Fractals
Fixed Point Theorems
Fractals
Harmonic Functions
Laplacian
Perron-Frobenius Theory
Self-Similar Energies
Product details
- ISBN 9789819809141
- Publication Date: 04 Nov 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
