On the $$\chi ^2$$ statistics of leading digits of irrational rotations with a large first or second partial quotient

2020 ◽  
Vol 80 (2) ◽  
pp. 158-171
Author(s):  
Toshifumi Nagayoshi ◽  
Keizo Takashima
Keyword(s):  
Partial Quotient ◽  
Irrational Rotations

REFLEXIVITY INDEX AND IRRATIONAL ROTATIONS

2021 ◽  
pp. 1-13
Author(s):  
BINGZHANG MA ◽  
K. J. HARRISON
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Irrational Rotations ◽  
Index 2

Abstract We determine the reflexivity index of some closed set lattices by constructing maps relative to irrational rotations. For example, various nests of closed balls and some topological spaces, such as even-dimensional spheres and a wedge of two circles, have reflexivity index 2. We also show that a connected double of spheres has reflexivity index at most 2.

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