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Let B be a Blaschke product for which the restriction to the unit circle [double-struck S]1 is a degree d > 1 covering. We prove that B is quasi-symmetrically conjugate to z ↣ zd on [double-struck S]1, if all its periodic points in [double-struck S]1 are repelling and if [double-struck S]1 does not intersect the ω-limit set of any recurrent critical point for B. [ABSTRACT FROM AUTHOR]

This paper concerns a class of monotone mappings, in a Hilbert space, that can be viewed as a nonlinear version of the class of positive invertible operators. Such mappings are proved to be open, locally Hölder continuous, and quasisymmetric. They arise naturally from the Beurling–Ahlfors extension and from Breniers polar factorization and find applications in the geometry of metric spaces and the theory of elliptic partial differential equations. [ABSTRACT FROM AUTHOR]