Category of Attractor and Its Application

Mansheng  Li; Yongjun  Li; Jinying  Wei

doi:10.4236/jamp.2015.37086

Jinying Wei, Yongjun Li, Mansheng Li

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.

Keywords: Ljusternik-Schnirelmann Category, Attractor, Attraction Basin

Cite this paper: Wei, J. , Li, Y. and Li, M. (2015) Category of Attractor and Its Application. Journal of Applied Mathematics and Physics, 3, 725-729. doi: 10.4236/jamp.2015.37086.

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