zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Iteration of analytic Euclidean contractions. (English) Zbl 0868.30027
Ali, Rosihan M. (ed.) et al., Computational methods and function theory 1994. Proceedings of the conference, Penang, Malaysia, March 21--25, 1994. Singapore: World Scientific. Ser. Approx. Decompos. 5, 57-74 (1995).
Summary: Let $D$ be a bounded convex domain and suppose that $f$ is an analytic map of $D$ into itself with $|f'|<1$. Then the diameter of $f^n(D)$ converges to zero and we obtain upper and lower estimates on the rate of this convergence. The methods used also give results in other circumstances; for example, for contractions of a domain in the $n$-dimensional Euclidean space. For the entire collection see [Zbl 0863.00033].

30D05Functional equations in the complex domain, iteration and composition of analytic functions
37F99Complex dynamical systems