Let f be an entire transcendental function of finite order and Delta be a forward invariant bounded Siegel disk for f with rotation number in Herman's class (Formula presented.). We show that if f has two singular values with bounded orbit, then the boundary of Δ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.

Singular values and bounded Siegel disks / Benini, A; Fagella, N. - In: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. - ISSN 0305-0041. - (2017). [10.1017/S0305004117000469]

Singular values and bounded Siegel disks

Benini a;
2017

Abstract

Let f be an entire transcendental function of finite order and Delta be a forward invariant bounded Siegel disk for f with rotation number in Herman's class (Formula presented.). We show that if f has two singular values with bounded orbit, then the boundary of Δ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.
Singular values and bounded Siegel disks / Benini, A; Fagella, N. - In: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. - ISSN 0305-0041. - (2017). [10.1017/S0305004117000469]
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: http://hdl.handle.net/11381/2867081
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact