ﻻ يوجد ملخص باللغة العربية
We develop a renormalization theory for analytic homeomorphisms of the circle with two cubic critical points. We prove a renormalization hyperbolicity theorem. As a basis for the proofs, we develop complex a priori bounds for multi-critical circle maps.
We show that for any $lambda in mathbb{C}$ with $|lambda|<1$ there exists an analytic expanding circle map such that the eigenvalues of the associated transfer operator (acting on holomorphic functions) are precisely the nonnegative powers of $lambda
We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural representation of the respective adjoint operators.
In this article, we show that R.H. Bings pseudo-circle admits a minimal non-invertible map. This resolves a problem raised by Bruin, Kolyada and Snoha in the negative. The main tool is the Denjoy-Rees technique, further developed by Beguin-Crovisier-
In this paper, we consider the renormalization operator $mathcal R$ for multimodal maps. We prove the renormalization operator $mathcal R$ is a self-homeomorphism on any totally $mathcal R$-invariant set. As a corollary, we prove the existence of the
In this note, we extend the renormalization horseshoe we have recently constructed with N. Goncharuk for analytic diffeomorphisms of the circle to their small two-dimensional perturbations. As one consequence, Herman rings with rotation numbers of bo