TY - JOUR

T1 - Lyapunov exponents for families of rotated linear cocycles

AU - Valenzuela-Henríquez, Pancho

AU - VASQUEZ EHRENFELD, CARLOS

PY - 2015/7/1

Y1 - 2015/7/1

N2 - 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 Rθ 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 Aθ 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 Aθ does not have dominated splitting is non empty.

AB - 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 Rθ 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 Aθ 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 Aθ does not have dominated splitting is non empty.

KW - cocycles

KW - Lyapunov exponents

KW - partial hyperbolicity

UR - http://www.scopus.com/inward/record.url?scp=84933056758&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/28/7/2423

DO - 10.1088/0951-7715/28/7/2423

M3 - Article

AN - SCOPUS:84933056758

VL - 28

SP - 2423

EP - 2440

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 7

ER -