## Institute for Mathematical Sciences

## Preprint ims91-1b

** Y. Jiang**
* Dynamics of Certain Smooth One-Dimensional Mappings II: Geometrically Finite One-Dimensional Mappings*

Abstract: We study geometrically finite one-dimensional mappings. These are a subspace of $C^{1+\alpha}$ one-dimensional mappings with
finitely many, critically finite critical points. We study
some geometric properties of a mapping in this subspace. We
prove that this subspace is closed under quasisymmetrical
conjugacy. We also prove that if two mappings in this subspace
are topologically conjugate, they are then quasisymmetrically
conjugate. We show some examples of geometrically finite
one-dimensional mappings.

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