ترغب بنشر مسار تعليمي؟ اضغط هنا

On computational complexity of Cremer Julia sets

196   0   0.0 ( 0 )
 نشر من قبل Artem Dudko
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We find an abundance of Cremer Julia sets of an arbitrarily high computational complexity.



قيم البحث

اقرأ أيضاً

160 - A. Blokh , L. Oversteegen 2008
We show that if $P$ is a quadratic polynomial with a fixed Cremer point and Julia set $J$, then for any monotone map $ph:Jto A$ from $J$ onto a locally connected continuum $A$, $A$ is a single point.
346 - A. Blokh , X. Buff , A.Cheritat 2008
In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of positive area such that for a full Lebesgue measure set of angles the imp ressions are degenerate, the Julia set is connected im kleinen at the landing points of these rays, and these points are contained in no other impression.
We show that there exist real parameters $c$ for which the Julia set $J_c$ of the quadratic map $z^2+c$ has arbitrarily high computational complexity. More precisely, we show that for any given complexity threshold $T(n)$, there exist a real paramete r $c$ such that the computational complexity of computing $J_c$ with $n$ bits of precision is higher than $T(n)$. This is the first known class of real parameters with a non poly-time computable Julia set.
A. Sannami constructed an example of the differentiable Cantor set embedded in the real line whose difference set has a positive measure. In this paper, we generalize the definition of the difference sets for sets of the two dimensional Euclidean spa ce as the sets of vectors between two sets, and estimate their measures. For the quadratic map Q_c(z)=z^2+c, we obtain that the measure of the difference set of its Julia set vanishes if |c|>3+sqrt{3}.
We give an introduction to buried points in Julia sets and a list of questions about buried points, written to encourage aficionados of topology and dynamics to work on these questions.
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