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The set of uniquely ergodic interval exchange transformations is path-connected

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Let $\unicode[STIX]{x1D70B}$ be a non-degenerate permutation on at least four symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\unicode[STIX]{x1D70B}$ is path-connected. Click to show full abstract

Let $\unicode[STIX]{x1D70B}$ be a non-degenerate permutation on at least four symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\unicode[STIX]{x1D70B}$ is path-connected.

Keywords: uniquely ergodic; interval exchange; ergodic interval; set uniquely; exchange transformations; path connected

Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2017

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