Abstract. We study the dynamics of continuous maps of the circle with periodic points. We show that the centre is the closure of the periodic points and that the depth of the centre is at most two. We also characterize the property that every power is transitive in terms of transitivity of a single power and some periodic data.
Abstract. For continuous maps / of the circle to itself, we show: (A) the set of nonwandering points of / coincides with that of / " for every odd n; (B) / has a horseshoe if and only if it has a non-wandering homoclinic point; (C) if the set of periodic points is closed and non-empty, then every non-wandering point is periodic.
Abstract.Let n and 6 be cyclic permutations of finite ordered sets. We say that n forces 6 if every continuous map of the interval which has a representative of n also has one of 6 . We give a geometric version of Jungreis' combinatorial algorithm for deciding in certain cases whether n forces 9 .
Abstract.Let n and 6 be cyclic permutations of finite ordered sets. We say that n forces 6 if every continuous map of the interval which has a representative of n also has one of 6 . We give a geometric version of Jungreis' combinatorial algorithm for deciding in certain cases whether n forces 9 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.