, Volume 96, Issue 4, pp 521-538

A shorter proof of the existence of the Feigenbaum fixed point

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Abstract

We use the Leray-Schauder Fixed Point Theorem to prove the existence of an analytic fixed point for the period doubling accumulation renormalization operator. Our argument does not, however, show that the linearization of the renormalization operator at this fixed point is hyperbolic.

Communicated by A. Jaffe