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.


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)


Zbl 0801.39005
Full Text: DOI


[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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