Smooth type 𝐼𝐼𝐼 diffeomorphisms of manifolds

Hawkins, Jane

doi:10.1090/S0002-9947-1983-0688966-0

Smooth type ${\rm III}$ diffeomorphisms of manifolds

Author: Jane Hawkins
Journal: Trans. Amer. Math. Soc. 276 (1983), 625-643
MSC: Primary 58F11; Secondary 28D99
DOI: https://doi.org/10.1090/S0002-9947-1983-0688966-0
MathSciNet review: 688966
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Abstract: In this paper we prove that every smooth paracompact connected manifold of dimension $\geqslant 3$ admits a smooth type ${\text{III}}_\lambda$ diffeomorphism for every $0 \leqslant \lambda \leqslant 1$ . (Herman proved the result for $\lambda = 1$ in [7].) The result follows from a theorem which gives sufficient conditions for the existence of smooth ergodic real line extensions of diffeomorphisms of manifolds.

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