{c}
{title2=$B_n(x,\epsilon)=\{y:d_n(x,y)<\epsilon\}$}

A radius-$\epsilon$ ball for a <Bowen metric> consists of the points whose first $n$ iterates stay within $\epsilon$ of the corresponding iterates of the centre. Balls at a fixed small radius distinguish forward <orbit> segments at that observational resolution.

Bowen ball

Entropy of a hyperbolic toral automorphism

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 16 / 3 / c / Solution

Bowen ball ( $B_{n} (x, ϵ) = {y : d_{n} (x, y) < ϵ}$ )

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Bowen ball (Bn​(x,ϵ)={y:dn​(x,y)<ϵ})

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Bowen ball ( $B_{n} (x, ϵ) = {y : d_{n} (x, y) < ϵ}$ )

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