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Fixed points of anti‐attracting maps and eigenforms on fractals

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  • Roberto Peirone

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.

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  • Roberto Peirone, 2021. "Fixed points of anti‐attracting maps and eigenforms on fractals," Mathematische Nachrichten, Wiley Blackwell, vol. 294(8), pages 1578-1594, August.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:8:p:1578-1594
    DOI: 10.1002/mana.201800093
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