Existence of Self-similar Energies on Finitely Ramified Fractals

Roberto Peirone (1)

1 DIPMAT - Dipartimento di Matematica [Roma II]

In this paper, I prove two existence results for regular eigenforms on finitely ramified fractals. The first result shows the existence of a regular eigenform for suitable weights, on fractals with the only assumptions that the boundary cells are separated and the union of the interior cells is connected. This result improves previous results, and works for many of the usually considered finitely ramified fractals. The second result shows the existence of a regular eigenform in the general case of finitely ramified fractals, in the setting considered, for example, in the book of Strichartz. In this more general case, however, the eigenform is not necessarily on the given structure, but on a suitable power of it. In any case, as the fractal generated is the same as the original fractal, the result provides a regular self-similar energy on the given fractal.

Mots clés: Fractals; Energies; Eigenforms

Domaines: Mathématiques générales [math.GM]

Roberto Peirone. Existence of Self-similar Energies on Finitely Ramified Fractals. 2011. ⟨hal-00628661⟩