منابع مشابه
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 with nonwandering set Ω(f) being the whole of M then f is expansive. This condition on the nonwandering set cannot be relaxed: we present an example of a 2-expansive homeomorphisms on a surface with genus 2 ...
متن کاملExpansive Homeomorphisms on Compact Manifolds
In this paper theorems are proved which provide for lifting and projecting expansive homeomorphisms through pseudocovering mappings so that the lift or projection is also an expansive homeomorphism. Using these techniques it is shown that the compact orientable surface of genus 2 admits an expansive homeomorphism.
متن کاملPositively expansive homeomorphisms of compact spaces
We give a new and elementary proof showing that a homeomorphism f : X → X of a compact metric space is positively expansive if and only if X is finite.
متن کاملLocal Product Structure for Expansive Homeomorphisms
Let f : M → M be an expansive homeomorphism with dense topologically hyperbolic periodic points, M a compact manifold. Then there is a local product structure in an open and dense subset of M . Moreover, if some topologically hyperbolic periodic point has codimension one, then this local product structure is uniform. In particular, we conclude that the homeomorphism is conjugated to a linear An...
متن کاملThe nonexistence of expansive homeomorphisms of chainable continua
A homeomorphism f : X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x 6= y, then there is an integer n ∈ Z such that d(f(x), f(y)) > c. In this paper, we prove that if a homeomorphism f : X → X of a continuum X can be lifted to an onto map h : P → P of the pseudoarc P , then f is not expansive. As a corollary, we prove that there are no expansive ho...
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ژورنال
عنوان ژورنال: General Topology and its Applications
سال: 1976
ISSN: 0016-660X
DOI: 10.1016/0016-660x(76)90021-0