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Smooth orbit equivalence of multidimensional Borel flows

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Abstract Free Borel R d -flows are smoothly equivalent if there is a Borel bijection between the phase spaces that maps orbits onto orbits and is a C ∞ -smooth… Click to show full abstract

Abstract Free Borel R d -flows are smoothly equivalent if there is a Borel bijection between the phase spaces that maps orbits onto orbits and is a C ∞ -smooth orientation preserving diffeomorphism between orbits. We show that all free non-tame Borel R d -flows are smoothly equivalent in every dimension d ≥ 2 . This answers a question of B. Miller and C. Rosendal.

Keywords: borel; borel flows; equivalence multidimensional; orbit equivalence; multidimensional borel; smooth orbit

Journal Title: Advances in Mathematics
Year Published: 2021

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