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

Let c be a real parameter in the Mandelbrot set, and f_c(z):= z^2 + c. Weprove a formula relating the topological entropy of f_c to the Hausdorffdimension of the set of rays landing on the real Julia set, and to theHausdorff dimension of the set of rays landing on the real section of theMandelbrot set, to the right of the given parameter c. We then generalize theresult by looking at the entropy of Hubbard trees: namely, we relate theHausdorff dimension of the set of external angles which land on a certain sliceof a principal vein in the Mandelbrot set to the topological entropy of thequadratic polynomial f_c restricted to its Hubbard tree.

Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set