# Commuting functions and simultaneous Abel equations

W. Jarczyk; K. Łoskot; M. C. Zdun

Annales Polonici Mathematici (1994)

- Volume: 60, Issue: 2, page 119-135
- ISSN: 0066-2216

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topW. Jarczyk, K. Łoskot, and M. C. Zdun. "Commuting functions and simultaneous Abel equations." Annales Polonici Mathematici 60.2 (1994): 119-135. <http://eudml.org/doc/262282>.

@article{W1994,

abstract = {The system of Abel equations
α(ft(x)) = α(x) + λ(t), t ∈ T,
is studied under the general assumption that $f_t$ are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.},

author = {W. Jarczyk, K. Łoskot, M. C. Zdun},

journal = {Annales Polonici Mathematici},

keywords = {Abel equation; commuting functions; iteration group; embeddability; family of commuting homeomorphisms; system of Abel equations; rational iteration group; continuous iteration group; Krylov-Bogolubov Theorem},

language = {eng},

number = {2},

pages = {119-135},

title = {Commuting functions and simultaneous Abel equations},

url = {http://eudml.org/doc/262282},

volume = {60},

year = {1994},

}

TY - JOUR

AU - W. Jarczyk

AU - K. Łoskot

AU - M. C. Zdun

TI - Commuting functions and simultaneous Abel equations

JO - Annales Polonici Mathematici

PY - 1994

VL - 60

IS - 2

SP - 119

EP - 135

AB - The system of Abel equations
α(ft(x)) = α(x) + λ(t), t ∈ T,
is studied under the general assumption that $f_t$ are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.

LA - eng

KW - Abel equation; commuting functions; iteration group; embeddability; family of commuting homeomorphisms; system of Abel equations; rational iteration group; continuous iteration group; Krylov-Bogolubov Theorem

UR - http://eudml.org/doc/262282

ER -

## References

top- [1] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monografie Mat. 61, Polish Scientific Publishers, Warszawa, 1982. Zbl0483.47038
- [2] W. Jarczyk, A recurrent method of solving iterative functional equations, Prace Naukowe Uniw. Śląsk. Katowic. 1206, Katowice, 1991. Zbl0741.39006
- [3] M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, Polish Scientific Publishers, Warszawa, 1968.
- [4] M. C. Zdun, Note on commutable functions, Aequationes Math. 36 (1988), 153-164. Zbl0662.39004
- [5] M. C. Zdun, On simultaneous Abel equations, Aequationes Math. 38 (1989), 163-177.
- [6] M. C. Zdun, On the orbits of disjoint groups of continuous functions, Rad. Mat., to appear.
- [7] M. C. Zdun, Some remarks on the iterates of commuting functions, in: European Conference on Iteration Theory, Lisbon, 1991, J. P. Lampreia et al. (eds.), World Scientific, Singapore, 1992, 336-342.