On linear cocycles over irrational rotations with secondary collisions

2021 ◽  
Author(s):  
Alexey V. Ivanov
Keyword(s):  
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.

scholarly journals Law of large numbers for certain cylinder flows

2013 ◽  
Vol 34 (3) ◽  
pp. 801-825 ◽  
Author(s):  
PATRÍCIA CIRILO ◽  
YURI LIMA ◽  
ENRIQUE PUJALS
Keyword(s):  
Gaussian Distribution ◽  
Law Of Large Numbers ◽  
Skew Product ◽  
Irrational Rotations ◽  
Large Numbers ◽  
Number Of Visits ◽  
Cylinder Flows

AbstractWe construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit a law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a Gaussian distribution.

On discrepancies of irrational rotations: an approach via rational rotation

2016 ◽  
Vol 75 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Naoto Shimaru ◽  
Keizo Takashima
Keyword(s):  
Irrational Rotations
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