# Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

## Abstract

In present work we study the entrance times for circle homeomorphisms with one break point and universal renormalization properties. Consider the set * X * of all orientation preserving circle homeomorphisms *T* with one break point and golden mean rotation number. It is well known that the renormalization group transformation has a unique periodic point * T _{b}* with period 2. Denote by

*B*the set of all circle maps

*C*-conjugated to

^{1 }*T*. Consider the map

_{ b}*T ∈ B*and its unique probability invariant measure

*μ*. Denote by

*E(x)*the first entrance times of

*x*to interval defined by generalized dynamical partition. Consider the rescaled first entrance time. We study convergence in law of random variables of rescaled first entrance time.

## First Page

209

## Last Page

221

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## Recommended Citation

Dzhalilov, Akhtam and Karimov, Javlon
(2020)
"The entrance times for circle maps with a break,"
*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*: Vol. 3:
Iss.
2, Article 10.

DOI: https://doi.org/10.56017/2181-1318.1097