## Institute for Mathematical Sciences

## Preprint ims92-5

** Y. Jiang**
* Dynamics of certain non-conformal semigroups*

Abstract: A semigroup generated by two dimensional $C^{1+\alpha}$ contracting maps is considered. We call a such semigroup
regular if the maximum $K$ of the conformal dilatations of
generators, the maximum $l$ of the norms of the derivatives of
generators and the smoothness $\alpha$ of the generators
satisfy a compatibility condition $K< 1/l^{\alpha}$. We prove
that the shape of the image of the core of a ball under any
element of a regular semigroup is good (bounded geometric
distortion like the Koebe $1/4$-lemma \cite{a}). And we use it
to show a lower and a upper bounds of the Hausdorff dimension
of the limit set of a regular semigroup. We also consider a
semigroup generated by higher dimensional maps.

View ims92-5 (PDF format)