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

In this paper we study arithmetic properties of a one-parameter family${\mathbf H}$ of H\'enon maps over the affine line. Given a family of initialpoints ${\mathbf P}$ satisfying a natural condition, we show the heightfunction $h_{{\mathbf P}}$ associated to ${\mathbf H}$ and ${\mathbf P}$ is therestriction of the height function associated to a semipositive adelicallymetrized line bundle on projective line. We then show various local propertiesof $h_{{\mathbf P}}$. Next we consider the set $\Sigma({\mathbf P})$ consistingof periodic parameter values, and study when $\Sigma({\mathbf P})$ is aninfinite set or not. We also study unlikely intersections of periodic parametervalues.

Heights and periodic points for one-parameter families of H\'enon maps