Abstract
A powerful theorem and construction of Lewis are used to construct three homeomorphisms on pseudoarcs, each of which admits wandering points. The first example has one attracting fixed point, one repelling fixed point, and all other points wander; the second has exactly one nonwandering point and all other points wander and have homoclinic orbits; and the third has a nonwandering set which separates the space. Also explored are how a pseudoarc homeomorphism that admits wandering points can sometimes induce a pseudoarc homeomorphism that (1) does not admit any wandering points, or (2) admits a dense open set of wandering points; how a pseudoarc can be turned inside-out; and what the existence of a homeomorphism that admits wandering points means for the homeomorphism group of a homogeneous continuum.
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