分形上反吸引映射的不动点与特征形
Fixed Points of anti-attracting maps and Eigenforms on Fractals
摘要：
分形分析中的一个重要问题是分叉分形上自相似能量的存在性。自相似能量是根据一个特殊的非线性算子的本征形，即本征向量构造的。以前的结果C。Sabot和V.Metz给出了特征形存在的条件。在本文中，我给出了一个不同的，可能更短的证明以前的结果，这似乎是适合于改进。这种证明是基于一个反吸引映射在凸集上的不动点定理。
英文摘要：
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 give a different and probably shorter proof of the previous results, which appears to be suitable for improvements. Such a proof is based on a fixed-point theorem for anti-attracting maps on a convex set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
