Monotonicity of entropy for real multimodal maps
Abstract
In Mil, Milnor posed the Monotonicity Conjecture that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected. This conjecture was proved for quadratic by Milnor & Thurston MT and for cubic maps by Milnor & Tresser, see MTr and also DGMT. In this paper we will prove the general case.
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