# Positive Lyapunov exponents for cocycles over time one anosov maps

## TL;DR

This paper proves that for a broad class of symplectic linear cocycles over time-one Anosov flows, positive Lyapunov exponents are typical for SRB measures, indicating prevalent chaotic behavior.

## Contribution

It establishes that positive Lyapunov exponents are generic for symplectic cocycles over time-one Anosov flows, expanding understanding of stability and chaos in dynamical systems.

## Key findings

- Positive Lyapunov exponents are dense in the space of cocycles.
- Generic cocycles over Anosov flows exhibit chaotic behavior.
- Results apply to SRB measures in the studied setting.

## Abstract

We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.