Multifractal formalism and anisotropic selfsimilar functions

Journal Article

• رابط المنشور على الويب: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/multifractal-for
• المجلة \ الصحيفة: Mathematical Proceedings of the Cambridge Philosophical Society

مستخلص المنشور

In this paper we prove that the conjectures of Frisch and Parisi and Arneodo et al. (called the multifractal formalism for functions) may fail for some non-homogeneous selfsimilar functions on ℝ2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modified.