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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