Recurrence and fixed points of surface homeomorphisms
1988 ◽
Vol 8
(8)
◽
pp. 99-107
◽
Keyword(s):
A Chain
◽
AbstractWe prove that if f is a homeomorphism of the annulus which is homotopic to the identity and has a compact invariant chain transitive set L, then either f has a fixed point or every point of L moves uniformly in one direction: clockwise or counterclockwise. If f is area-preserving, then the annulus itself is a chain transitive set, so, in the presence of a boundary twist condition, one obtains a fixed point. The same techniques apply to homeomorphisms of the torus T2. In this setting we show that if f is homotopic to the identity, preserves Lebesgue measure and has mean translation 0, then it has at least one fixed point.
1990 ◽
Vol 10
(2)
◽
pp. 209-229
◽
Keyword(s):
1987 ◽
Vol 7
(3)
◽
pp. 463-479
◽
Keyword(s):
Keyword(s):
2013 ◽
Vol 155
(1)
◽
pp. 87-99
◽
2008 ◽
Vol 77
(1)
◽
pp. 37-48
◽
Keyword(s):
Keyword(s):