Differentiability of Lyaupnov Exponents
  We prove differentiability of certain linear combinations of the Lyapunov spectra of a flow on a principal bundle of a semi-simple Lie group. The specific linear combinations that yield differentiability are determined by the finest Morse decomposition on the flag bundles. Differentiability is taken with respect to a differentiable structure on the gauge group, which is a Banach-Lie group. 
Thiago F. Ferraiol and Luiz A. B. San Martin
math.DS