Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling

Mestel, B. D.; Osbaldestin, A. H. and Tsygvintsev, A. V. (2004). Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling. Communications in Mathematical Physics, 250(2) pp. 241–257.

DOI: https://doi.org/10.1007/s00220-004-1143-2

Abstract

We establish rigorous bounds for the unstable eigenvalue of the period-doubling renormalization operator for asymmetric unimodal maps. Herglotz-function techniques and cone invariance ideas are used. Our result generalizes an established result for conventional period doubling.

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