Mathematical Citation Quotient (MCQ) 2018: 0.40
On the Boundary of the Set of the Closure of Contractive Polynomials
For and a = (a 1, . . . , ad ) T ∈ ℤ d , let τ r(a) = (a 2, . . . , ad , –⌊r T a⌋) T . Further, let . In this paper we prove that if some roots of the polynomial Xd + rdX d–1 + ⋯ + r 2 X + r 1 are t -th roots of unity and the others lie in the open unit disc, then |a k+t – ak | < c 1 with a constant c 1 which does not depend on k. Under some conditions this yields an algorithm to decide whether the sequence is, for all a, ultimately periodic, or becomes divergent for some a.
We study the boundary of the closure of 𝒟3 and show that large parts of it belong to 𝒟3, while others lie outside 𝒟3.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.