# Some aspects of the local theory of generalized Dhombres functional equations in the complex domain

ESAIM: Proceedings (2012)

- Volume: 36, page 1-14
- ISSN: 1270-900X

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topTomaschek, Jörg. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Some aspects of the local theory of generalized Dhombres functional equations in the complex domain ." ESAIM: Proceedings 36 (2012): 1-14. <http://eudml.org/doc/251225>.

@article{Tomaschek2012,

abstract = {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.},

author = {Tomaschek, Jörg},

editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},

journal = {ESAIM: Proceedings},

keywords = {Generalized Dhombres equation; Iterative functional equation; generalized Dhombres equation; iterative functional equation},

language = {eng},

month = {8},

pages = {1-14},

publisher = {EDP Sciences},

title = { Some aspects of the local theory of generalized Dhombres functional equations in the complex domain },

url = {http://eudml.org/doc/251225},

volume = {36},

year = {2012},

}

TY - JOUR

AU - Tomaschek, Jörg

AU - Fournier-Prunaret, D.

AU - Gardini, L.

AU - Reich, L.

TI - Some aspects of the local theory of generalized Dhombres functional equations in the complex domain

JO - ESAIM: Proceedings

DA - 2012/8//

PB - EDP Sciences

VL - 36

SP - 1

EP - 14

AB - 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.

LA - eng

KW - Generalized Dhombres equation; Iterative functional equation; generalized Dhombres equation; iterative functional equation

UR - http://eudml.org/doc/251225

ER -

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