ﻻ يوجد ملخص باللغة العربية
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 full renormalization horseshoe for multimodal maps.
As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension 3, we introduce a $C^2$-open set of diffeomorphisms of whose cross sections are Cantor sets; the intersection of the unstable and stable sets contains a fract
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
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.
In this paper, we consider weak horseshoe with bounded-gap-hitting times. For a flow $(M,phi)$, it is shown that if the time one map $(M,phi_1)$ has weak horseshoe with bounded-gap-hitting times, so is $(M,phi_tau)$ for all $tau eq 0$. In addition, w
The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also d