Dynamics of generic multidimensional linear differential systems

Bessa, Mário

http://hdl.handle.net/10400.2/13860

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Bessa, Mário

Abstract(s)

We prove that there exists a residual subset R (with respect to the C^0 topology) of d-dimensional linear differential systems based in a μ-invariant flow and with transition matrix evolving in GL(d, R) such that if A ∈ R, then, for μ-a.e. point, the Oseledets splitting along the orbit is dominated (uniform projective hyperbolicity) or else the Lyapunov spectrum is trivial. Moreover, in the conservative setting, we obtain the dichotomy: dominated splitting versus zero Lyapunov exponents.