## Institute for Mathematical Sciences

## Preprint ims91-12a

** Y. Jiang**
* Dynamics of Certain Smooth One-Dimensional Mappings III: Scaling Function Geometry*

Abstract: We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional
mapping. This scaling function is discontinuous. We prove that
the scaling function and the asymmetries at the critical points
of a geometrically finite one-dimensional mapping form a
complete set of $C^{1}$-invariants within a topological
conjugacy class.

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