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

Consider the one-parameter family of cubic polynomials defined by $f_t(z)=-\frac 32 t(-2z^3+3z^2)+1, t \in \mathbb{C}_2$. This family corresponds to aslice of the parameter space of cubic polynomials in $\mathbb{C}_2[z]$. Weinvestigate which parameters in this family belong to the cubic $2$-adicMandelbrot set, a $p$-adic analog of the classical Mandelbrot set. When $t=1$,$f_t(z)$ is post-critically finite with a strictly preperiodic critical orbit.We establish that this is a non-isolated boundary point on the cubic $2$-adicMandelbrot set and show asymptotic self-similarity of the Mandelbrot set nearthis point. Subsequently, we investigate the Julia set for polynomial on theboundary and demonstrate a similarity between the Mandelbrot set at this pointand the Julia set, similar to what is seen in the classical complex case.

On a Slice of the Cubic 2-adic Mandelbrot Set