


On the
general solution of the system of cocycle equations without
regularity conditions 
On the general solution of the system of cocycle equations
without regularity conditions
Jointly written with LUDWIG REICH.
Aequationes
mathematicae 68, 200  229, 2004.
Abstract: We describe the general solution
(α,β), where α=(α(s,x))_{s∈
ℂ} and β=(β(s,x))_{s∈ ℂ}
are families of formal power series in C[[x]], of the two
socalled cocycle equations
α(s+t,x)= α(s,x)α(t,π(s,x)),
s,t∈ ℂ 
(Co1) 

β(s+t,x)=
β(s,x)α(t,π(s,x)) +β(t,π(s,x)),
s,t∈ ℂ 
(Co2) 

together with the boundary condition
where π=(π(s,x))_{s∈ ℂ} is an iteration
group in C[[x]]. Our method is based on the knowledge of the
regular solutions of (Co1) and (Co2) and on a wellknown and often
used theorem concerning the algebraic relations between exponential
functions and additive functions.
harald.fripertinger "at" unigraz.at, October 10,
2019






GDPR 
On the
general solution of the system of cocycle equations without
regularity conditions 

