TITLE:
Category of Attractor and Its Application
AUTHORS:
Jinying Wei, Yongjun Li, Mansheng Li
KEYWORDS:
Ljusternik-Schnirelmann Category, Attractor, Attraction Basin
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.7,
June
30,
2015
ABSTRACT:
In this paper, we provide a new approach to
study the geometry of attractor. By applying category, we investigate the
relationship between attractor and its attraction basin. In a complete metric
space, we prove that the categories of attractor and its attraction basin are
always equal. Then we apply this result to both autonomous and non-autonomous
systems, and obtain a number of corresponding results.