arXiv subjects

Raquel Saraiva

Publications and source records attributed to Raquel Saraiva.

2 recordsLinked to original sources

arXiv2026

Discontinuity example for the Lyapunov exponents on the boundary of the uniformly hyperbolic set

We present an example of a discontinuity point for the Lyapunov exponents when viewed as a function of the cocycle in a topology finer than the $C^0$-topology. The linear cocycle taking values in SL(2,R) is locally constant, defined over a Bernoulli shift, and lies on the boundary of the uniformly hyperbolic set. In particular, we show that it can be approximated, in the $C_{δ-\log}$-topology, by cocycles whose Lyapunov exponents vanish.

math.DS↗

arXiv2026

Discontinuity of Lyapunov exponents for SL$(2,\mathbb{R})$ valued cocycles

We exhibit an example of discontinuity point for the Lyapunov exponents as a function of the cocycle in the $α$-Hölder topology. The linear cocycle taking values in $SL(2, \mathbb{R})$ is locally constant and defined over a Bernoulli shift. Our example extends Bocker-Viana's and Butler's results. In particular, it gives a partial answer to a question raised by Clark Butler. Finally, we give an example of discontinuity in the setting of $SL(m,\mathbb{R})$-valued cocycles, which is constructed from $SL(2, \mathbb{R})$-valued cocycles.

math.DS↗