A local but not global attractor for a Z n-symmetric map

• Type: Article in International Scientific Journal
• Date: 2012

Authors

Alarcon, B (Author) Other; Castro, SBSD (Author) FEP; Labouriau, IS (Author) FCUP

Journal

Title: Journal of Singularities

Vol. 6

Pages: 1-14

ISSN: 1949-2006

Publisher: Worldwide Center of Mathematics

Indexing

ISI Web of Knowledge

Scopus - 5 Citations

Other information

Authenticus ID: P-008-639

DOI: 10.5427/jsing.2012.6a

Abstract (EN): There are many tools for studying local dynamics. An important problem is how this information can be used to obtain global information. We present examples for which local stability does not carry on globally. To this purpose we construct, for any natural n ≿2, planar maps whose symmetry group is ℿ n having a local attractor that is not a global attractor. The construction starts from an example with symmetry group ℿ 4. We show that although this example has codimension 3 as a ℿ 4-symmetric map-germ, its relevant dynamic properties are shared by two 1-parameter families in its universal unfolding. The same construction can be applied to obtain examples that are also dissipative. The symmetry of these maps forces them to have rational rotation numbers.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14