MULTIFRACTAL ANALYSIS FOR EXPANDING INTERVAL MAPS WITH INFINITELY MANY BRANCHES

作者：Fan, Ai-Hua^*; Jordan, Thomas; Liao, Lingmin; Rams, Michal

来源：Transactions of the American Mathematical Society, 2015, 367(3): 1847-1870.

• Multifractal analysis
• Birkhoff averages
• interval maps
• infinitely many branches

In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.

• 出版日期2015-3
• 单位华中师范大学