Twelve open problems on the exact value of the Hausdorff measure and on topological entropy: a brief survey of recent results**Project partially supported by the National Natural Science Foundation of China, the Foundation of Guangdong Province and the Foundation of Zhongshan University Advanced Research Center.

Abstract

Twelve open problems and one conjecture are posed in this exposition. Among them, eight open problems and the conjecture are on calculation of the exact value of the Hausdorff measure of self-similar sets, and four open problems are on topological entropy. We give a brief survey of the recent research results related to these open problems and conjecture.