Expanding direction of the period doubling operator

Details Expanding direction of the period doubling operator Expanding direction of the period doubling operator

1991-03-28

arxiv.org/abs/math/9201281v1

Mathematics

Dynamical Systems

Scientific paper

10.1007/BF02099180

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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