Fixed points of anti‐attracting maps and eigenforms on fractals

Roberto Peirone

Mathematische Nachrichten, 2021, vol. 294, issue 8, 1578-1594

Abstract: An important problem in analysis on fractals is the existence of a self‐similar energy on finitely ramified fractals. The self‐similar energies are constructed in terms of eigenforms, that is, eigenvectors of a special nonlinear operator. Previous results by C. Sabot and V. Metz give conditions for the existence of an eigenform. In this paper, I prove this type of result in a different way. The proof given in this paper is based on a general fixed‐point theorem for anti‐attracting maps on a convex set.

Date: 2021
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