Home > ACTATTPU > Vol. 8 (2019) > Iss. 3

## Acta of Turin Polytechnic University in Tashkent

#### Abstract

Let h be a piecewise-linear (PL) circle homeomorphism with two break points a0 , c0 and irrational rotation number ρh . Denote by qn , n ≥ 1 the first return times of h and 000(0)():(0)hhaahaσ′−=′+ the jump of h at the point a0 . We prove that for every 1xS∈ the sequence 01log()mod1,1log()nqhDhxnaσ≥ is uniformly distributed on [0,1].

#### First Page

12

#### Last Page

15

#### References

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#### Recommended Citation

Dzhalilov, Akhtam and Tashkulov, Khamza
(2018)
"Uniform Distribution for Piecewise-Linear Herman's Maps with Two Breaks,"
*Acta of Turin Polytechnic University in Tashkent*: Vol. 8
:
Iss.
3
, Article 2.

Available at:
https://uzjournals.edu.uz/actattpu/vol8/iss3/2