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**On some invariants of conjugacy of disjoint iteration groups.**
*(English)*
Zbl 0830.39009

The first part of the paper provides a full description of disjoint iteration groups of continuous self-mappings of an open real interval. This is a completion of the author’s result [Aequationes Math. 46, No. 1- 2, 19-37 (1993; Zbl 0801.39005)]. The main results (Theorems 1 and 2) give a characterization of conjugacy of disjoint iteration groups formulated in terms of the parameters of the preceding description. Proving them the author determines all homeomorphisms conjugated to the groups under consideration. A complete system of invariants of disjoint groups is also found and a method of determination of the invariants is presented.

Reviewer: W.Jarczyk (Katowice)

### MSC:

39B12 | Iteration theory, iterative and composite equations |

39B62 | Functional inequalities, including subadditivity, convexity, etc. |

37C10 | Dynamics induced by flows and semiflows |

26A18 | Iteration of real functions in one variable |

54H20 | Topological dynamics (MSC2010) |

### Citations:

Zbl 0801.39005
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\textit{M. C. Zdun}, Result. Math. 26, No. 3--4, 403--410 (1994; Zbl 0830.39009)

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### References:

[1] | M. Bajger, M. C. Zdun, On rational flows of continuous functions, Proceedings of European Conference on Iteration Theory, Batschuns 1992, World Scientific, Singapore-New Jersey-London-Hong Kong (to appear). · Zbl 0918.58061 |

[2] | W. Jarczyk, K. Łoskot, M. C. Zdun, Commuting functions and simultaneous Abels equations, Ann. Polon. Math. (to appear). · Zbl 0828.39006 |

[3] | K. Kuratowski, A. Mostowski, Set Theory, Warszawa-Amsterdam-New York-Oxford 1976. |

[4] | F. Neumann, On transformations of differential equations and systems with deviating arguments, Czech Math. J. 31(106) (1981), 87–90. |

[5] | F. Neumann, Simultaneous solutions of a system of Abel equations and differential equations with several deviation, Czech Math. J. 32(107) (1982), 488–494. |

[6] | M. C. Zdun, The structure of iteration groups of continuous functions, Aequationes Math. 46 (1993), 19–37. · Zbl 0801.39005 |

[7] | M. C. Zdun, On the orbits of disjoint groups of continuous functions, Radovi Math. 8/1 (to appear). |

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