报告人：张振亮副教授 河南科技学院

报告题目: Hausdorff dimension faithfulness of expansions of real numbers

报告摘要：On one hand, for continued fraction expansion, Oppenheim expansion and $Q_{\infty}$-expansion, we show that,the family of all possible unions of finite consecutive cylinders of the same rank of expansion is faithful for the Hausdorff dimension calculation on the unit interval. On the other hand, for Oppenheim expansion, we show the family of all possible unions of finite consecutive cylinders of the same rank is faithful. Some special cases such as L\"{u}roth expansion, Engel expansion and Sylvester expansion are included.

For $Q_{\infty}$-expansion, we give a necessary and sufficient condition for the family of all cylinders of the $Q_{\infty}$-expansion to be faithful for Hausdorff dimension calculation on the unit interval. This answers an open problem mentioned in “On the fractal phenomena connected with infinite linear IFs” by S. Albeverio, Y. Kondratiev, R. Nikiforov, G. Torbin.

报告时间：2017年7月10日(星期一)上午10：25-11：10

报告地点: 科技楼南楼602室