On Invariant Decompositions, Dominated Splittings and Sectional-Hyperbolicity

Details On Invariant Decompositions, Dominated Splittings and Sectional-Hyperbolicity On Invariant Decompositions, Dominated Splittings and Sectional-Hyperbolicity

2011-03-29

arxiv.org/abs/1103.5637v5

Mathematics

Dynamical Systems

15 pages, 5 figures; bibliographical reference corrected; proof of a lemma simplified; generalized assumptions of main theorem

Scientific paper

For a $C^1$ flow $X_t$ on a compact manifold $M$ and a compact invariant subset $\Lambda$, with a $DX_t$-invariant splitting $E\oplus F$ of the tangent bundle $T_\Lambda M$ over $\Lambda$, we consider the relation between weak forms of hyperbolicity along each subbundle and domination. We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a $C^1$ flow $X_t$ to be dominated. This allows us to redefine sectional-hyperbolicity for compact invariant subsets of $C^1$ flows with no domination assumption.

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