HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS
2014 ◽
Vol 98
(3)
◽
pp. 375-389
◽
Keyword(s):
Let${\it\gamma}$be a hyperbolic closed orbit of a$C^{1}$vector field$X$on a compact$C^{\infty }$manifold$M$and let$H_{X}({\it\gamma})$be the homoclinic class of$X$containing${\it\gamma}$. In this paper, we prove that if a$C^{1}$-persistently expansive homoclinic class$H_{X}({\it\gamma})$has the shadowing property, then$H_{X}({\it\gamma})$is hyperbolic.
Keyword(s):
Keyword(s):
2019 ◽
Vol 16
(11)
◽
pp. 1950180
◽
1991 ◽
Vol 11
(3)
◽
pp. 443-454
◽
2011 ◽
Vol 13
(02)
◽
pp. 191-211
◽
Keyword(s):
1995 ◽
Vol 05
(03)
◽
pp. 895-899
◽
Keyword(s):
2021 ◽
Vol 62
◽
pp. 53-66
2015 ◽
Vol 12
(10)
◽
pp. 1550111
◽
Keyword(s):