## Institute for Mathematical Sciences

## Preprint ims91-6

** Y. Jiang, T. Morita, & D. Sullivan**
* Expanding Direction of the Period Doubling Operator.*

Abstract: We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a
``Perron-Frobenius type operator'', to study the linearization
of the period doubling operator at its fixed point. We then use
a sequence of linear operators with finite ranks to study this
induced operator. The proof is constructive. One can calculate
the expanding direction and the rate of expansion of the period
doubling operator at the fixed point.

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