Multifractal Analysis on Averaged Conformal Repeller
班榮超 教授國立東華大學應用數學系 上午 10:00–10:50 S4 2樓數學與理論物理中心In this talk, we will introduce the concept of multifractal analysis on dynamical systems, which become a popular topic in dimension theory and has wide applications on the researches of turbulence, distribution of galaxies and biology. Next, we prove that C1 averaged conformal repeller admits the multifractal analysis of dimension spectrum by comparing the variational formula of L. Barreira and D. Feng, here, the dynamical system is only needed C1. Finally, we show that the equilibrium measure of variational principle is weak Gibbs, these two results generalize the work of L. Barreira for 2-D case and D. Feng for conformal case.