✦ LIBER ✦
On conditions guaranteeing that mappings are elements of iteration groups
✍ Scribed by Krzysztof Ciepliński
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 207 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
In this note, we prove that if F = {f v : I -→ I, v ∈ V } is a suitable iteration group on an open interval I and a function g : I -→ I is continuous at least at one point and commutes with two mappings f a , f b ∈ F such that b a is irrational, then g ∈ F . If, moreover, f a < id < f b , then the commutativity of g with f a and f b can be replaced by the inequalities
As an application of the obtained results, we give a contribution to Schwaiger's problem concerning iteration groups which are commuting in pairs.