Abstract: We will discuss the dynamics of linear cocycles over chaotic dynamical systems. We establish the existence of cocycles that Cα-stably exhibit ``fiberwise bounded orbits'' for α> 0. This result is achieved through a novel mechanism that induces stable elliptic-type behavior in GL(d, R) and SL(d, R) cocycles. Furthermore, we demonstrate that this phenomenon is C0-dense among SL(d, R) cocycles over shifts of finite type without dominated splitting. This leads to a new dichotomy for generic linear cocycles over shift maps.
This is joint work with H. Rajabzadeh and Z. Reshadat.
