Topological dimension of singular - hyperbolic attractors
نویسنده
چکیده
An attractor is a transitive set of a flow to which all positive orbit close to it converges. An attractor is singular-hyperbolic if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction [16]. The geometric Lorenz attractor [6] is an example of a singular-hyperbolic attractor with topological dimension ≥ 2. We shall prove that all singular-hyperbolic attractors on compact 3-manifolds have topological dimension ≥ 2. The proof uses the methods in [15].
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