A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents

A hyperbolicity notion for linear differential equations , t∈[t−,t+], is defined which unifies different existing notions like finite-time Lyapunov exponents (Haller, 2001, [13], , Shadden et al., 2005, [24], ), uniform or M-hyperbolicity (Haller, 2001, [13], , Berger et al., 2009, [6], ) and (t−,(t+−t−))-dichotomy (Rasmussen, 2010, [21], ). Its relation to the dichotomy spectrum (Sacker and Sell, 1978, [23], , Siegmund, 2002, [26], ), D-hyperbolicity (Berger et al., 2009, [6]) and real parts of the eigenvalues (in case A is constant) is described. We prove a spectral theorem and provide an approximation result for the spectral intervals.