Singular hyperbolicity of star flows on surfaces

Authors
Zhu, Sheng Zhi
Citation
Zhu, Sheng Zhi, Singular hyperbolicity of star flows on surfaces, Acta mathematica Sinica. English series (Print) , 31(9), 2015, pp. 1415-1423
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
31
Issue
9
Year of publication
2015
Pages
1415 - 1423
Database
ACNP
SICI code
Abstract
In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.