## Abstract

Consider a compact metric space X, a homeomorphism T: X → X and an ergodic T-invariant measure μ. In this work, we are interested in the study of the upper Lyapunov exponent λ^{+}(θ) associated to the periodic family of cocycles defined by where is a linear cocycle orientation-preserving and R_{θ} is a rotation of angle θεℝ. We show that if the cocycle A has dominated splitting, then there exists a non empty open set of parameters θ such that the cocycle A_{θ} has dominated splitting and the function is real analytic and strictly concave. As a consequence, we obtain that the set of parameters θ where the cocycle A_{θ} does not have dominated splitting is non empty.

Original language | English |
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Pages (from-to) | 2423-2440 |

Number of pages | 18 |

Journal | Nonlinearity |

Volume | 28 |

Issue number | 7 |

DOIs | |

State | Published - 1 Jul 2015 |

Externally published | Yes |

## Keywords

- Lyapunov exponents
- cocycles
- partial hyperbolicity