Homeomorphisms of the circle were first considered by Poincare* who used them to obtain qualitative results for a class of differential equations on the torus. He classified those which have a denseâ€¦ (More)

1. Preliminaries. Let Y be a topological space and let G be a topological group. A transformation group (Y, G) is a continuous mapping 7r of YÃ— G into Y such that zr(y, e) = y for all y (e = identityâ€¦ (More)

Our purpose is to determine the maximum number of distinct recurrent orbit closures which can occur in a continuous flow on a compact nonorientable surface. Let X be a surface and let R be the realâ€¦ (More)

In this note we present a new p r o o f o f the classical t heo rem that a transitive h o m e o m o r p h i s m o f the circle is topologically equ iva len t to a rotat ion t h rough an angleâ€¦ (More)

1. Introduction. Let X be a topological space and let 0 be a homeo-morphism of X onto X. The pair (X, <j>) is called a cascade. A nonempty subset M of X is a minimal subset of (X, 0) if M is closed,â€¦ (More)