Abstract
The rigorous treatment of period-doubling cascades, developed by Lanford for analytic families, is extended to coverC 2+α families for any α>0. This requires spectral analysis of the linearised doubling operator on spaces of differentiable mappings, and a version of stable manifold theory which takes account of the non-differentiability of the doubling operator on these spaces.
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Communicated by J.-P. Eckmann
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Davie, A.M. Period doubling forC 2+∈ mappings. Commun.Math. Phys. 176, 261–272 (1996). https://doi.org/10.1007/BF02099549
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DOI: https://doi.org/10.1007/BF02099549