Mathematical Research Letters

Volume 28 (2021)

Number 3

A new example of robustly transitive diffeomorphism

Pages: 665 – 679

DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n3.a2

Authors

Pablo D. Carrasco (Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil)

Davi Obata (Department of Mathematics, University of Chicago, Illinois, U.S.A.)

Abstract

We present an example of a $\mathcal{C}^1$-robustly transitive skew-product with non-trivial, non-hyperbolic action on homology. The example is conservative, ergodic, non-uniformly hyperbolic and its fiber directions cannot be decomposed into two dominated subbundles.

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D. Obata was supported by the ERC project 692925 NUHGD.

Received 9 May 2019

Accepted 12 June 2020

Published 2 June 2021