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/

Zendy Plus

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

Zendy Tools

Zendy Open

For the quadratic family $f_{c}(z) = z^2+c$ with $c$ in the exterior of theMandelbrot set, it is known that every point in the Julia set movesholomorphically. Let $\hat{c}$ be a semi-hyperbolic parameter in the boundaryof the Mandelbrot set. In this paper we prove that for each $z = z(c)$ in theJulia set, the derivative $dz(c)/dc$ is uniformly $O(1/\sqrt{|c-\hat{c}|})$when $c$ belongs to a parameter ray that lands on $\hat{c}$. We alsocharacterize the degeneration of the dynamics along the parameter ray.

From Cantor to Semi-hyperbolic Parameter along External Rays