Self-similar Energies On Finitely Ramified Fractals
Seiten
2025
World Scientific Europe Ltd (Verlag)
978-1-80061-687-5 (ISBN)
World Scientific Europe Ltd (Verlag)
978-1-80061-687-5 (ISBN)
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Analysis of 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. A self-similar fractal is a non-empty, compact subset ℱ of a metric space (X, d) that satisfies ℱ = kSi=1ψi(ℱ) where ψi are a finite number of contractive similarities. 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.
| Erscheint lt. Verlag | 21.5.2025 |
|---|---|
| Verlagsort | London |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-80061-687-2 / 1800616872 |
| ISBN-13 | 978-1-80061-687-5 / 9781800616875 |
| Zustand | Neuware |
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