|
A counterexample to the ``composition conjecture"
Author(s):
F.
Pakovich
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3747-3749.
MSC (2000):
Primary 34C99;
Secondary 30D05
Posted:
June 13, 2002
MathSciNet review:
1920083
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this note we construct a class of counterexamples to the ``composition conjecture" concerning an infinitesimal version of the center problem for the polynomial Abel equation in the complex domain.
References:
-
- 1.
- M. Briskin, J.-P. Francoise, Y. Yomdin, Center conditions, compositions of polynomials and moments on algebraic curve, Ergodic Theory Dyn. Syst. 19 (1999), no. 5, 1201-1220. MR 2000k:34051
- 2.
- M. Briskin, J.-P. Francoise, Y. Yomdin, Center condition II: Parametric and model center problems, Isr. J. Math. 118 (2000), 61-82. MR 2001j:34033
- 3.
- M. Briskin, J.-P. Francoise, Y. Yomdin, Center condition III: Parametric and model center problems, Isr. J. Math. 118 (2000), 83-108. MR 2001j:34034
- 4.
- C. Christopher, Abel equations: composition conjectures and the model problem, Bull. Lond. Math. Soc. 32 (2000), no. 3, 332-338. MR 2001d:34047
- 5.
- N. Roytvarf, Generalized moments, composition of polynomials and Bernstein classes, in ``Entire functions in modern analysis. B.Ya. Levin memorial volume", to appear.
- 6.
- A. Schinzel, Polynomials with special regard to reducibility, Encyclopedia of Mathematics and Its Applications 77, Cambridge University Press, 2000. MR 2001h:11135
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
34C99,
30D05
Retrieve articles in all Journals with
MSC (2000):
34C99,
30D05
Additional Information:
F.
Pakovich
Affiliation:
Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Email:
pakovich@wisdom.weizmann.ac.il
DOI:
10.1090/S0002-9939-02-06755-2
PII:
S 0002-9939(02)06755-2
Keywords:
Poincare center-focus problem,
polynomial Abel equation,
polynomials,
compositions,
functional equations
Received by editor(s):
January 22, 2002
Received by editor(s) in revised form:
February 22, 2002
Posted:
June 13, 2002
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
|
