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Blenders near polynomial product maps of C².
- Source :
- Journal of the European Mathematical Society (EMS Publishing); 2021, Vol. 23 Issue 11, p3555-3589, 35p
- Publication Year :
- 2021
-
Abstract
- In this paper we show that if p is a polynomial which bifurcates then the product map (z,w)↦(p(z),q(w)) can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types: repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets: the bifurcation locus of Hd(P²) and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of Hénon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
BIFURCATION theory
ENDOMORPHISMS
SET theory
PERTURBATION theory
Subjects
Details
- Language :
- English
- ISSN :
- 14359855
- Volume :
- 23
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- Journal of the European Mathematical Society (EMS Publishing)
- Publication Type :
- Academic Journal
- Accession number :
- 157482131
- Full Text :
- https://doi.org/10.4171/JEMS/1076