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

Given a fixed-point free compact holomorphic self-map $f$ on a boundedsymmetric domain $D$, which may be infinite dimensional, we establish theexistence of a family $\{H(\xi, \lambda)\}_{\lambda >0}$ of convex$f$-invariant domains at a point $\xi$ in the boundary $\partial D$ of $D$,which generalises completely Wolff's theorem for the open unit disc in$\mathbb{C}$. Further, we construct horoballs at $\xi$ and show that they areexactly the $f$-invariant domains when $D$ is of finite rank. Consequently, weshow in the latter case that the limit functions of the iterates $(f^n)$ withweakly closed range all accumulate in one single boundary component of$\partial D$.

Horoballs and iteration of holomorphic maps on bounded symmetric domains