Self-similar Energies On Finitely Ramified Fractals
Series: Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications; 9;
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65 467 Ft
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Product details:
- Publisher World Scientific
- Date of Publication 4 November 2025
- ISBN 9789819809141
- Binding Hardback
- No. of pages492 pp pages
- Language English 651
Categories
Long description:
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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