Expansive homeomorphisms in continuum theory

There Are No Stable Points for Continuum-Wise Expansive Homeomorphisms

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 ...

Expansive 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.

Chaotic continua of (continuum-wise) expansive homeomorphisms and chaos in the sense of Li and Yorke

A homeomorphism f : X → X of a compactum X is expansive (resp. continuum-wise expansive) if there is c > 0 such that if x, y ∈ X and x 6= y (resp. if A is a nondegenerate subcontinuum of X), then there is n ∈ Z such that d(f(x), f(y)) > c (resp. diam f(A) > c). We prove the following theorem: If f is a continuum-wise expansive homeomorphism of a compactum X and the covering dimension of X is po...

Positively 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.