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Generic invariant measures for minimal iterated function systems of homeomorphisms of the circle

Volume 124 / 2020

Wojciech Czernous Annales Polonici Mathematici 124 (2020), 33-46 MSC: Primary 37E10; Secondary 60G30, 37C20. DOI: 10.4064/ap180518-12-4 Published online: 10 October 2019


It is shown that the set of iterated function systems having an absolutely continuous invariant measure is negligible in the family of all systems of circle homeomorphisms satisfying the condition that the finite generator system has a proper subset, acting minimally, and having no measure invariant simultaneously for all its maps.


  • Wojciech CzernousInstitute of Oceanography
    Faculty of Oceanography and Geography
    University of Gdańsk
    Marszałka Józefa Piłsudskiego 47
    81-378 Gdynia, Poland

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