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 C1 -conjugated to T b . Consider the map 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