In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on theâ€¦ (More)

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the wellknown notions of non-wandering, topologically transitive, and topologicallyâ€¦ (More)

We give a new and elementary proof showing that a homeomorphism f : X â†’ X of a compact metric space is positively expansive if and only if X is finite.

A novel mononuclear germylene, Ge[1,8-((i)PrN)(2)C(10)H(6)] (1), was isolated as a stable crystalline solid by the reaction of Li(2)[1,8-((i)PrN)(2)C(10)H(6)] with GeCl(2)(1,4-dioxane). Structuralâ€¦ (More)

We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contractionâ€¦ (More)

We introduce the notions of weakly and strongly positively expansive (wPE and sPE, respectively) discrete dynamical systems. Both are topological generalizations of the well-known metric notion ofâ€¦ (More)

ACM supports a number of special interest groups, or SIGs, that you as a member can join. SIGs provide an opportunity for people who are interested in a particular area of computer science to comeâ€¦ (More)

We examine the itinerary of 0 âˆˆ S = R/Z under the rotation by Î± âˆˆ R\Q. The motivating question is: if we are given only the itinerary of 0 relative to I âŠ‚ S, a finite union of closed intervals, canâ€¦ (More)