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Self-similar Energies On Finitely Ramified Fractals - Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications Peirone, Roberto (University Of Rome Tor Vergata, Italy)
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Self-similar Energies On Finitely Ramified Fractals - Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications
Peirone, Roberto (University Of Rome Tor Vergata, Italy)
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.
| Media | Books Hardcover Book (Book with hard spine and cover) |
| Released | November 4, 2025 |
| ISBN13 | 9789819809141 |
| Publishers | World Scientific Publishing Co Pte Ltd |
| Pages | 492 |
| Dimensions | 150 × 220 × 20 mm · 857 g |
