Unique non-integer base expansions: old and new

[TMCSC]

Oct 17-31, 2020

腾讯会议（线上）

ID: 873 3382 9397     Password: 202020

[minicourse]孔德荣2001017-31-01.png

SPEAKER

孔德荣（重庆大学）

ABSTRACT

Expansions in non-integer bases can be dated back to the pioneering works of Renyi (1957) and Parry (1960). After almost 30 years of silence, Erdos et al (1990) reinvestigated this topic from a more combinatorial way, and afterwards it got a great attention from different branches of mathematics. In this short course we will talk about some recent progress on this topic, in particular on the unique non-integer base expansions. We will study the set of points with a unique expansion in some non-integer base from the topological and dimensional perspectives. We will also study the set of univoque bases such that a given number has a unique expansion. Furthermore, we will investigate the corresponding bifurcation sets. As applications we will consider (1) the intersections of large Cantor sets, (2) the density spectrum of Cantor measures, (3) the singularities of Okamoto’s self-affine functions, and (4) the set related to Bernoulli convolutions.

SUPPORTED BY

国家天元数学西南中心

四川大学数学学院

VIDEOS

  • Unique solvability of weakly homogeneous generalized variational inequalities
  • 14:30 - 15:30, 2020-08-04 at 腾讯会议（线上）
  • 黄正海（天津大学）
  • Unique non-integer base expansions: old and new I
  • 09:30 - 11:30, 2020-10-17 at 腾讯会议（线上）
  • 孔德荣（重庆大学）
  • Unique non-integer base expansions: old and new II
  • 09:30 - 11:30, 2020-10-18 at 腾讯会议（线上）
  • 孔德荣（重庆大学）
  • Unique non-integer base expansions: old and new III
  • 09:30 - 11:30, 2020-10-24 at 腾讯会议（线上）
  • 孔德荣（重庆大学）
  • Unique non-integer base expansions: old and new IV
  • 09:30 - 11:30, 2020-10-25 at 腾讯会议（线上）
  • 孔德荣（重庆大学）
  • Unique non-integer base expansions: old and new V
  • 09:30 - 11:30, 2020-10-31 at 腾讯会议（线上）
  • 孔德荣（重庆大学）