Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Fixed points of commuting holomorphic mappings other than the Wolff point


Author: Filippo Bracci
Journal: Trans. Amer. Math. Soc. 355 (2003), 2569-2584
MSC (2000): Primary 30D05; Secondary 30C80, 30E25, 47B33
Published electronically: January 29, 2003
MathSciNet review: 1974004
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $\Delta$ be the unit disc of $\mathbb C$ and let $f,g \in \mathrm{Hol}(\Delta,\Delta)$ be such that $f \circ g = g \circ f$. For $A>1$, let $\mathrm{Fix}_A (f):=\{p \in \partial\Delta \mid \lim_{r \to 1}f(rp)=p, \lim_{r \to 1}\vert f'(rp)\vert\leq A \}$. We study the behavior of $g$ on $\mathrm{Fix}_A (f)$. In particular, we prove that $g(\mathrm{Fix}_A (f))\subseteq \mathrm{Fix}_A (f)$. As a consequence, besides conditions for $\mathrm{Fix}_A(f) \cap \mathrm{Fix}_A(g) \neq \emptyset$, we prove a conjecture of C. Cowen in case $f$ and $g$ are univalent mappings.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30D05, 30C80, 30E25, 47B33

Retrieve articles in all journals with MSC (2000): 30D05, 30C80, 30E25, 47B33


Additional Information

Filippo Bracci
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Email: fbracci@mat.uniroma2.it

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03170-2
PII: S 0002-9947(03)03170-2
Keywords: Fixed points; Wolff point; commuting mappings
Received by editor(s): April 1, 2001
Published electronically: January 29, 2003
Additional Notes: Partially supported by Progetto MURST di Rilevante Interesse Nazionale Proprietà geometriche delle varietà reali e complesse and GNSAGA
Article copyright: © Copyright 2003 American Mathematical Society