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It is given notions of singular hyperbolicity and sectional Lyapunovexponents of orders beyond the classical ones, namely, other dimensions besidesthe dimension 2 and the full dimension of the central subbundle of the singularhyperbolic set. It is obtained a characterization of dominated splittings,partial and singular hyperbolicity in this broad sense, by using Lyapunovexponents and the notion of infinitesimal Lyapunov functions. Furthermore, itis given alternative requirements to obtain singular hyperbolicity. As anapplication we obtain some results related to singular hyperbolic sets forflows.

Singular Hyperbolicity and sectional Lyapunov exponents of various orders