2020/02/17 by Nicolas Gourmelon, Gourmelon, Nicolas · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #28Dxx #34C23 #34C37 #34K18 #37Cxx #37Dxx #37Gxx #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2002.06783
openalex publication_date 2020/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show how the small perturbations of a linear cocycle have a relative rotation number associated with an invariant measure of the base dynamics an with a 2-dimensional bundle of the finest dominated splitting (provided that some orientation is preserved). Likewise small perturbations of diffeomorphisms have a relative rotation number associated with an invariant measure supported in a hyperbolic set and with a 2-dimensional bundle as above. The properties of that relative rotation number allow some steps towards dichotomies between complex eigenvalues and dominated splittings in higher dimensions and higher regularity. We also prove that generic smooth linear cocycles above a full-shift (and actually above infinite factors of transitive subshift of finite type) admit a periodic point with simple Lyapunov spectrum.