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On fractional iterates of a homeomorphism of the plane

100%

Leśniak Z.

2002

tom 79

nr 2

129-137

We find all continuous iterative roots of nth order of a Sperner homeomorphism of the plane onto itself.

On homeomorphic and diffeomorphic solutions of the Abel equation on the plane

100%

Leśniak Z.

1993

tom 58

nr 1

7-18

We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.

On conjugacy equation in dimension one

63%

Ciepliński K. , Leśniak Z.

Banach Center Publications

2013

tom 99

nr 1

31-44

In this paper, recent results on the existence and uniqueness of (continuous and homeomorphic) solutions φ of the equation φ ∘ f = g ∘ φ (f and g are given self-maps of an interval or the circle) are surveyed. Some applications of these results as well as the outcomes concerning systems of such equations are also presented.