Abstract
A volume hyperbolic set is a compact invariant set with a dominated splitting whose external bundles uniformly contract and expand the volume respectively [1]. Examples of volume hyperbolic sets for diffeomorphisms or flows are the hyperbolic sets, the geometric Lorenz attractor [3] and the singular horseshoe [6]. We shall prove that no invariant subset of a volume hyperbolic set of a three-dimensional flow is homeomorphic to a closed surface.
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