# A new example of robustly transitive diffeomorphism

## TL;DR

This paper introduces a novel example of a $ ext{C}^1$-robustly transitive skew-product system that is conservative, ergodic, and non-uniformly hyperbolic, with unique non-hyperbolic homological action.

## Contribution

It provides the first known example of a robustly transitive skew-product with non-hyperbolic homology action and complex fiber dynamics.

## Key findings

- The system is $ ext{C}^1$-robustly transitive.
- The system is conservative and ergodic.
- Fiber directions lack dominated splitting.

## 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 expanded/contracted bundles.