Examples of diffeomorphism group cocycles with no periodic approximation
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- by Sebastian Hurtado PDF
- Proc. Amer. Math. Soc. 147 (2019), 3797-3802
Abstract:
We construct a finitely generated subgroup of $\operatorname {Diff}^{\infty }(\mathbb {S}^3 \times \mathbb {S}^1)$ where every element is conjugate to an isometry but such that the group action itself is far from isometric (the group has “exponential growth of derivatives”). As a corollary, one obtains a locally constant $\operatorname {Diff}^{\infty }(\mathbb {S}^3 \times \mathbb {S}^1)$ valued cocycle over a hyperbolic dynamical system which has elliptic behavior over its periodic orbits but which preserves a measure with non-zero top fiber-Lyapunov exponent. Additionally, we provide new examples of Banach cocycles not satisfying the periodic approximation property as first shown in Ergodic Theory Dynam. Systems 39 (2019), pp. 689–706.References
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Additional Information
- Sebastian Hurtado
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 1120207
- Email: shurtados@uchicago.edu
- Received by editor(s): May 25, 2017
- Received by editor(s) in revised form: December 7, 2017
- Published electronically: June 14, 2019
- Communicated by: Nimish Shah
- © Copyright 2019 Sebastian Hurtado
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3797-3802
- MSC (2010): Primary 37C85
- DOI: https://doi.org/10.1090/proc/14103
- MathSciNet review: 3993772