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- W2079427440 abstract "For a pair of points x, y in a compact, Riemannian manifold M let n t (x, y) (resp. s t (x, y)) be the number of geodesic segments with length ≤ t joining these points (resp. the minimal number of point obstacles needed to block these geodesic segments). We study relationships between the growth rates of n t (x, y) and s t (x, y) as t → ∞. We obtain lower bounds on s t (x, y) in terms of the topological entropy h(M) and the fundamental group π 1(M). For instance, we show that if h(M) > 0 then s t grows exponentially, with the rate at least h(M)/2. This strengthens earlier results on blocking of geodesics (Burns and Gutkin Discrete Contin Dyn Syst 21:403–413, 2008; Lafont and Schmidt Geom Topol 11:867–887, 2007), and puts them in a new perspective." @default.
- W2079427440 created "2016-06-24" @default.
- W2079427440 creator A5090415767 @default.
- W2079427440 date "2008-10-07" @default.
- W2079427440 modified "2023-10-14" @default.
- W2079427440 title "Topological entropy and blocking cost for geodesics in Riemannian manifolds" @default.
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- W2079427440 doi "https://doi.org/10.1007/s10711-008-9296-3" @default.
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