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

• Tipo: Artigo em Revista Científica Internacional
• Data: 2012

Autores

Alarcon, B (Autor) Outra; Castro, SBSD (Autor) FEP; Labouriau, IS (Autor) FCUP

Revista

Título: Journal of Singularities

Vol. 6

Páginas: 1-14

ISSN: 1949-2006

Editora: Worldwide Center of Mathematics

Indexação

ISI Web of Knowledge

Scopus - 5 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14