English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a compact, polynomially convex, regular set $K \subset\mathbb{C}$ and a sequence $(p_n)_{n=1}^\infty$ of polynomials with uniformlybounded zeros and such that $\lim_{n \to \infty}\|p_n\|_K^{1/({\rm deg} \p_n)}={\rm cap}(K)$, where ${\rm cap}(K)$ is the logarithmic capacity of $K$.Taking an arbitrary sequence $(d_k)_{k=1}^\infty$ of integers greater than $1$we prove that there exists a nonempty set$\mathcal{K}[(p_{d_k})_{k=1}^\infty]$, depending only on the sequence$(p_{d_k})_{k=1}^\infty$, such that for any compact polynomially convex regularset $E$ the preimages $(p_{d_k}\circ...\circ p_{d_1})^{-1}(E)$ converge inKlimek's metric to $\mathcal{K}[(p_{d_k})_{k=1}^\infty]$. We call the set$\mathcal{K}[(p_{d_k})_{k=1}^\infty]$ the non-autonomous filled Julia setgenerated by the polynomial sequence $(p_{d_k})_{k=1}^\infty$. Our toy exampleis generated by $t_n=\frac{1}{2^{n-1}}T_n,\ n\in\{1,2,...\}$, associated with$K=[-1,1]$, where $T_n$ is the classical Chebyshev polynomial of degree $n$.

Non-autonomous Julia sets for sequences of polynomials satisfying Kalm\'ar-Walsh theorem