Geodesic
Some aspects of the local theory of generalized Dhombres functional equations in the complex domain
Jörg Tomaschek1
1 Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstraße 36, A-8010 Graz, Austria
ESAIM. Proceedings, Tome 36 (2012), pp. 1-14 Cet article a éte moissonné depuis la source EDP Sciences

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We study the generalized Dhombres functional equation f(zf(z)) = ϕ(f(z)) in the complex domain. The function ϕ is given and we are looking for solutions f with f(0) = w0 and w0 is a primitive root of unity of order l ≥ 2. All formal solutions for this case are described in this work, for the situation where ϕ can be transformed into a function which is linearizable and local analytic in a neighbourhood of zero we also show that we obtain local analytic solutions. We also discuss an example where it is possible to use other methods than we use in the general case.
DOI : 10.1051/proc/201236001

Jörg Tomaschek 1

1 Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstraße 36, A-8010 Graz, Austria 
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     title = {Some aspects of the local theory of generalized {Dhombres} functional equations in the complex domain},
     journal = {ESAIM. Proceedings},
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     doi = {10.1051/proc/201236001},
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Jörg Tomaschek. Some aspects of the local theory of generalized Dhombres functional equations in the complex domain. ESAIM. Proceedings, Tome 36 (2012), pp. 1-14. doi: 10.1051/proc/201236001

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