437 research outputs found
On homeomorphisms with the two-sided limit shadowing property
We prove that the two-sided limit shadowing property is among the strongest
known notions of pseudo-orbit tracing. It implies shadowing, average shadowing,
asymptotic average shadowing and specification properties. We also introduce a
weaker notion that is called two-sided limit shadowing with a gap and prove
that it implies shadowing and transitivity. We show that those two properties
allow to characterize topological transitivity and mixing in a class of
expansive homeomorphisms and hence they characterize transitive (mixing) shifts
of finite type.Comment: 1 figure, comments are welcome
Partially Expansive Homeomorphisms
In this article we consider several forms of expansivity. We introduce two
new definitions related with topological dimension. We study the topology of
local stable sets under cw-expansive surface homeomorphisms and expansive
homeomorphisms of three-manifolds. The problem of -stable expansivity is
also considered
N-expansive homeomorphisms on surfaces
We exploit the techniques developed in [Le] to study N-expansive
homeomorphisms on surfaces. We prove that when f is a 2-expansive homeomorphism
defined on a compact boundaryless surface M without wandering points then f is
expansive. This condition on the wandering set cannot be relaxed: we present an
example of a 2-expansive homeomorphisms on the bitorus with wandering points
that is not expansive
There are no stable points for continuum-wise expansive homeomorphisms
We obtain some results about continuum-wise expansive homeomorphisms, such as
non-existence of stable points and presence of non-trivial connected components
within the local stable and unstable sets. These facts have been of importance
in theorems of classification of expansive homeomorphisms. They are achieved
now, however, by new and self contained techniques that hold on more general
settings.Comment: 7 pages, 1 figur
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