ترغب بنشر مسار تعليمي؟ اضغط هنا

Critical points on the boundaries of Siegel disks

51   0   0.0 ( 0 )
 نشر من قبل ul
 تاريخ النشر 1995
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Let $f$ be a polynomial map of the Riemann sphere of degree at least two. We prove that if $f$ has a Siegel disk $G$ on which the rotation number satisfies a diophantine condition, then the boundary of $G$ contains a critical point.



قيم البحث

اقرأ أيضاً

As was recently shown by the first author and others, golden-mean Siegel disks of sufficiently dissipative complex quadratic Henon maps are bounded by topological circles. In this paper we investigate the geometric properties of such curves, and demonstrate that they cannot be $C^1$-smooth.
63 - Jonguk Yang 2020
Consider a polynomial $f$ of degree $d geq 2$ that has a Siegel disk $Delta_f$ with a rotation number of bounded type. We prove that there does not exist a hedgehog containing $Delta_f$. Moreover, if the Julia set $J_f$ of $f$ is connected, then it i s locally connected at the Siegel boundary $partial Delta_f$.
We prove that a long iteration of rational maps is expansive near boundaries of bounded type Siegel disks. This leads us to extend Petersens local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case.
139 - Jonguk Yang 2014
Consider a quadratic polynomial with a fixed Siegel disc of bounded type. Using an adaptation of complex a priori bounds for critical circle maps, we prove that this Siegel polynomial is conformally mateable with the basilica polynomial.
We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invarian t probability measure with exponential decay of correlations for H{o}lder observations.
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