Mathematical Research Letters

Volume 28 (2021)

Number 3

A new example of robustly transitive diffeomorphism

Pages: 665 – 679



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.)


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.

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

Received 9 May 2019

Accepted 12 June 2020

Published 2 June 2021