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.

中文翻译：

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分形上反吸引图和特征形式的固定点

分形分析中的一个重要问题是有限分形上自相似能量的存在。自相似能量是根据特征形式构造的，即特殊非线性算子的特征向量。C. Sabot 和 V. Metz 的先前结果给出了存在特征形式的条件。在本文中，我以不同的方式证明了这种类型的结果。本文给出的证明是基于凸集上反吸引图的一般不动点定理。