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Journal Articles Journal of modern dynamics Year : 2016

An Urysohn-type theorem under a dynamical constraint

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Albert Fathi
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Abstract

We address the following question raised by M. Entov and L. Polterovich: given a continuous map f:X→X of a metric space X, closed subsets A,B⊂X, and an integer n≥1, when is it possible to find a continuous function θ:X→ℝ such that θf−θ≤1,θ∣∣A≤0,andθ∣∣B>n? To keep things as simple as possible, we solve the problem when A is compact. The non-compact case will be treated in a later work.

Dates and versions

ensl-01412052 , version 1 (07-12-2016)

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Albert Fathi. An Urysohn-type theorem under a dynamical constraint. Journal of modern dynamics, 2016, ⟨10.3934/jmd.2016.10.331⟩. ⟨ensl-01412052⟩
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