Geodesic
On solutions of functional equations determining subsemigroups of $L^1_4$
Janina Chodukowska 1   ; Zbigniew Marciniak 2
1 Al. Jana Pawła II 3/72 37-450 Stalowa Wola, Poland
2 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 181-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $L_4^1$ be the group of 4-jets at zero of diffeomorphisms $f$ of $\mathbb{R}$ with $f(0)=0$. Identifying jets with sequences of derivatives, we determine all subsemigroups of $L_4^1$ consisting of quadruples $(x_1,f(x_1,x_4),g(x_1,x_4),x_4)\in(\mathbb{R}\setminus\{0\})\times\mathbb{R}^3$ with continuous functions $f,g\colon(\mathbb{R}\setminus\{0\})\times\mathbb{R}\to\mathbb{R}$. This amounts to solving a set of functional equations.
DOI : 10.4064/cm119-2-2
Keywords: group jets zero diffeomorphisms mathbb identifying jets sequences derivatives determine subsemigroups consisting quadruples mathbb setminus times mathbb continuous functions colon mathbb setminus times mathbb mathbb amounts solving set functional equations

Janina Chodukowska  1   ; Zbigniew Marciniak  2

1 Al. Jana Pawła II 3/72 37-450 Stalowa Wola, Poland
2 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Janina Chodukowska; Zbigniew Marciniak. On solutions of functional equations determining subsemigroups of $L^1_4$. Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 181-192. doi: 10.4064/cm119-2-2

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