We prove that if a holomorphic self-map $fcolon Omega o Omega$ of a bounded strongly convex domain $Omegasubset mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball $mathbb B^k$. We also obtain the dual result for a holomorphic self-map $fcolon Omega o Omega$ with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of $f$ via the squeezing function.

Canonical models on strongly convex domains via the squeezing function

Amedeo Altavilla;
2020-01-01

Abstract

We prove that if a holomorphic self-map $fcolon Omega o Omega$ of a bounded strongly convex domain $Omegasubset mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball $mathbb B^k$. We also obtain the dual result for a holomorphic self-map $fcolon Omega o Omega$ with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of $f$ via the squeezing function.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/265192
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact