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 ...
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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 کاملExpansive Homeomorphisms with the Shadowing Property on Zero Dimensional Spaces
Let X = {a}∪ {ai | i ∈ N} be a subspace of Euclidean space E such that limi→∞ ai = a and ai 6= aj for i 6= j. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y ) of all homeomorphisms on Y , where Y = {a, b} ∪ {...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1982-0671230-8