Characterization of uniform hyperbolicity for fiber-bunched cocycles

Speaker(s)

Reza Mohammadpour Bejargafsheh

Affiliation

IM PAN

Date

Nov. 9, 2018, 10:15 a.m.

Room

room 5840

Seminar

Seminar of Dynamical Systems Group

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Let $(T;A)$ be a $SL(2;\mathbb{R})$-cocycle defined over a transitive subshift of finite type. We will show that the cocycle $(T;A)$ is uniformly hyperbolic if the cocycle satisfies the fiber-bunching condition, and there is a constant $\tau > 0$ and a full probability set $\mathcal{S}\subset \mathbb{R}$ such that $\lambda_{+}(x)\geq \tau$ for every $x \in \mathcal{S}$.

The talk follows the proofs of R.Velozo Ruiz MSc dissertation, based on C. Bonatti, X. Gómez-Mont, M. Viana's paper and M. Viana's book.

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