A note on some iterative roots

Paweł Solarz

Abstract


In this paper some orientation-preserving iterative roots of an orientation-preserving homeomorphism F: S1→ S1 which possess periodic points of order n are considered. Namely, iterative roots with periodic points of order n. All orders of such roots are determined and their general construction is given.

Keywords


iteration, iterative root, periodic point

Mathematics Subject Classification


39B12;26A18

References


Bajger, M. "On the structure of some flows on the unit circle." Aequationes Math. 55 (1998): 106-121.

Ciepliński, K. "The rotation number of the composition of homeomorphisms." Rocznik Nauk.-Dydakt. Prace Mat. 17 (2000): 83-87.

Cornfeld, I.P., S.V. Fomin and Y.G. Sinai. "Ergodic theory." Grundlehren Math. Wiss. 245. Berlin, Heidelberg, New York: Spirnger-Verlag, 1982.

Kuczma, M., B. Choczewski and R. Ger. "Iterative functional equations." Encyclopaedia Math. Appl. 32. Cambridge: Cambridge Univ. Press, 1990.

Melo, W. de, and S. van Strien. "One-dimensional dynamics.' Ergeb. Math. Grenzgeb. (3). Band 25. Berlin: Springer-Verlag, 1993.

Solarz, P. "On some iterative roots." Publ. Math. Debrecen 63 (2003): 677-692.

Solarz, P. "On some properties of orientation-preserving surjections on the circle." Math. Slovaca 57.6 (2007): 1-14.

Zdun, M.C. "On conjugacy of homeomorphisms of the circle possessing periodic points." J. Math. Anal. Appl. 330 (2007): 51-65.

Zdun, M.C. "On a factorization of homeomorphisms of the circle possessing periodic points." J. Math. Anal. Appl. 342 (2008): 340-348.


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