Some duality properties of non-saddle sets



Downloads per month over past year

Giraldo, A. and Morón, Manuel A. and Romero Ruiz del Portal, Francisco and Rodríguez Sanjurjo, José Manuel (2001) Some duality properties of non-saddle sets. Topology and its Applications, 113 (1-3). pp. 51-59. ISSN 0166-8641

[thumbnail of 18.pdf] PDF
Restringido a Repository staff only


Official URL:


We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting-that the Conley index of a regular isolated non-saddle set is determined, in certain cases, by its shape. We finally introduce and study the notion of dual of a non-saddle set. Examples of compacta related by duality are attractor-repeller pairs. We use the complement theorems in shape theory to prove that the shape of the dual set is determined by the shape of the original non-saddle set.

Item Type:Article
Uncontrolled Keywords:Dynamical system; isolated set; non-saddle set; shape
Subjects:Sciences > Mathematics > Topology
ID Code:15410
Deposited On:29 May 2012 11:35
Last Modified:12 Dec 2018 15:13

Origin of downloads

Repository Staff Only: item control page