On iterative convexity of diffeomorphism |
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Authors: | Marek Cezary Zdun |
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Affiliation: | 1. Institute of Mathematics, Pedagogical University, Kraków, Poland.mczdun@up.krakow.pl |
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Abstract: | AbstractA function f is said to be iteratively convex if f possesses convex iterative roots of all orders. We give several constructions of iteratively convex diffeomorphisms and explain the phenomenon that the non-existence of convex iterative roots is a typical property of convex functions. We show also that a slight perturbation of iteratively convex functions causes loss of iterative convexity. However, every convex function can be approximate by iteratively convex functions. |
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Keywords: | Convex functions iterations semi-flows semi-group iterative roots dyadic numbers |
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