Self-similar Energies On Finitely Ramified Fractals

Roberto Peirone (Autor)

Buch | Hardcover

492 Seiten

2025
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-98-0914-1 (ISBN)

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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.

Erscheinungsdatum	14.10.2025
Reihe/Serie	Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications ; 9
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	981-98-0914-2 / 9819809142
ISBN-13	978-981-98-0914-1 / 9789819809141
Zustand	Neuware