Guckenheimer, John Limit sets of S-unimodal maps with zero entropy. (English) Zbl 0625.58027 Commun. Math. Phys. 110, 655-659 (1987). One-dimensional mappings “at the limit of period doubling” are studied in this paper without the use of the renormalization theory of Feigenbaum and others. The principal result is that the attracting part of the nonwandering set is a Cantor set of measure zero under the additional assumption that the map has negative Schwarzian negative. Cited in 15 Documents MSC: 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems Keywords:period doubling; renormalization theory of Feigenbaum; nonwandering set; Schwarzian negative PDF BibTeX XML Cite \textit{J. Guckenheimer}, Commun. Math. Phys. 110, 655--659 (1987; Zbl 0625.58027) Full Text: DOI OpenURL References: [1] Feigenbaum, M.: Universal behavior in nonlinear systems, Los Alamos Sci.1, 4-29 (1980) [2] Guckenheimer, J.: Sensitive dependence to initial conditions for one dimensional maps. Commun. Math. Phys.70, 133-160 (1979) · Zbl 0429.58012 [3] Singer, D.: Stable orbits and bifurcations of maps of the interval. SIAM J. Appl. Math.35, 260-267 (1978) · Zbl 0391.58014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.