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