Abstract
This paper studies the iteration of maps of the interval which have negative Schwarzian derivative and one critical point. The maps in this class are classified up to topological equivalence. The equivalence classes of maps which display sensitivity to initial conditions for large sets of initial conditions are characterized.
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Communicated by D. Ruelle
Research partially supported by the National Science Foundation and the Volkswagen Foundation. We gratefully acknowledge this support and the hospitality of the Courant Institute for Mathematical Sciences and the Institut des Hautes Études Scientifiques
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Guckenheimer, J. Sensitive dependence to initial conditions for one dimensional maps. Commun.Math. Phys. 70, 133–160 (1979). https://doi.org/10.1007/BF01982351
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DOI: https://doi.org/10.1007/BF01982351