Let L¹₄ be the group of 4-jets at zero of diffeomorphisms f of ℝ with f(0) = 0. Identifying jets with sequences of derivatives, we determine all subsemigroups of L¹₄ consisting of quadruples (x₁,f(x₁,x₄),g(x₁,x₄),x₄) ∈ (ℝ∖{0}) × ℝ³ with continuous functions f,g:(ℝ∖{0}) × ℝ → ℝ. This amounts to solving a set of functional equations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-2,
author = {Janina Chodukowska and Zbigniew Marciniak},
title = {On solutions of functional equations determining subsemigroups of L14},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {181-192},
zbl = {1191.39024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-2}
}
Janina Chodukowska; Zbigniew Marciniak. On solutions of functional equations determining subsemigroups of L¹₄. Colloquium Mathematicae, Tome 120 (2010) pp. 181-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-2/