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)
Contact bifurcations related to critical sets and focal points in iterated maps of the plane. (English) Zbl 1242.39024
Liz, Eduardo (ed.) et al., Proceedings of the workshop on future directions in difference equations, Vigo, Spain, June 13–17, 2011. Vigo: Servizo de Publicacións da Universidade de Vigo (ISBN 978-84-8158-541-4/pbk). Colección Congresos 69, 15-50 (2011).
Summary: In this survey article we briefly describe some properties of difference equations obtained by the iterated applications of two-dimensional maps of the plane and we try to characterize the qualitative changes (or bifurcations) of the asymptotic behavior of the solutions, as some parameters are varied, in terms of contacts between particular curves and invariant sets which characterize the global properties of the iterated maps. In particular we consider the role of critical curves in noninvertible maps of the plane and the contacts involving focal points and prefocal sets in maps of the plane characterized by the presence (in the map or in some inverse map) of a denominator that vanishes along a curve of the plane. The effects of the global bifurcations given by contacts involving such singular curves on the attractors and their basins are described through some examples.
39A28Bifurcation theory (difference equations)
39-02Research monographs (functional equations)
39A10Additive difference equations
37G35Attractors and their bifurcations
39A12Discrete version of topics in analysis