@article{Doan2012,
Abstract = {A hyperbolicity notion for linear differential equations $\dot{x} = A(t)x$, $t\in[t_-,t_+]$ , 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.},
Author = {{D}oan, {T}. {S}. and {K}arrasch, {D}. and {N}guyen, {T}. {Y}. and {S}iegmund, {S}.},
Doi = {10.1016/j.jde.2012.02.002},
Issn = {0022-0396},
Journal = {J. Differential Equations},
Keywords = {Finite-time dynamics, Finite-time Lyapunov Exponent, Hyperbolicity, Spectral theorem, Transient behavior},
Number = {10},
Pages = {5535--5554},
Title = {{A} unified approach to finite-time hyperbolicity which extends finite-time {Lyapunov} exponents},
Volume = {252},
Year = {2012}}