Self-similar Energies On Finitely Ramified Fractals

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 where copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive.This monograph outlines 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.

Product details

• Authors: Roberto Peirone
• Publisher: Ingram Publishers Services
• Languages: English
• Product format: Hardback
• Release: 20.07.2025
• EAN: 9789819809141
• ISBN: 978-981-9809-14-1
• Series: Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / Differential Equations / General, MATHEMATICS / Functional Analysis, MATHEMATICS / Measurement, Functional analysis & transforms, Functional analysis and transforms, Fractal geometry