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PM functions, their characteristic intervals and iterative roots

100%

Zhang W.

Annales Polonici Mathematici

1996-1997

tom 65

nr 2

119-128

The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.

Continuous solutions of a polynomial-like iterative equation with variable coefficients

100%

Zhang W. , Baker J. A.

Annales Polonici Mathematici

2000

tom 73

nr 1

29-36

Using the fixed point theorems of Banach and Schauder we discuss the existence, uniqueness and stability of continuous solutions of a polynomial-like iterative equation with variable coefficients.

On iterative roots of homeomorphisms of the circle

63%

Zdun M.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

tom Vol. 48, no 2

203--213

In this paper we deal with the problem of existence and uniqueness of continuous iterative roots of homeomorphisms of the circle. Let F : [S^1 --> S^1] be a homeomorphism without periodic points. If the limit set of the orbit [F^k(z), k belongs to Z] equals [S^1], then F has exactly n iterative roots of n-th order. Otherwise F either has no iterative roots of n-th order or F has infinitely many iterative roots depending on an arbitrary function. In this case we determined all iterative roots of n-th order of F.

Set-valued iterative square roots of bijections

51%

Powierża T.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

tom Vol. 47, no 4

377--383

There are different ideas how to generalize the notion of an iterative root, especially when a function does not have a "real" root. We consider a multifunction as a substitute for this notion.