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There are infinitely many initial points in with this Lyapunov exponent. For example, all the numbers , that is, all the numbers whose continued fractions ultimately end in

One might ask if there are non-noble numbers with this
Lyapunov exponent, and indeed I think the answer is yes. The trick to
this is constructing numbers with lots of **1**'s in the continued
fraction. For example, ,
where there are **1**'s in between the 2's, might work.
I do not know of
a good characterization of the set of all such noble-equivalent or
`nearly noble'
numbers.
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