ترغب بنشر مسار تعليمي؟ اضغط هنا

The full renormalization horseshoe for multimodal maps

77   0   0.0 ( 0 )
 نشر من قبل Yimin Wang
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Yimin Wang




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

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 al set of Hausdorff dimension nearly $1$. Our proof employs the thicknesses of Cantor sets.
280 - Michael Yampolsky 2021
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 unded type survive on a codimension one set of parameters under small two-dimensional perturbations.
117 - Michael Yampolsky 2019
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.
114 - Leiye Xu , Junren Zheng 2019
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 e prove that for an affine homeomorphsim of a compact metric abelian group, positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.
70 - Diana A. Mendes 2003
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 efine a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computation of the topological entropy of two-dimensional triangular maps. The connection between kneading theory and subshifts of finite type is shown by using a commutative diagram derived from the homological configurations associated to $m-$modal maps of the interval.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا