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

Abstract

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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.

How to cite

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W. 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

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

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