We showed earlier that the separation of orbits initially close to each other occurred at an exponential rate. We would like to examine the Lyapunov exponents of the Gauss map, to see if we can explicitly measure the rate of separation. The Lyapunov exponents of orbits of the Gauss map are defined as [8]

whenever this limit exists. Note that exists even at the jump discontinuities , but there is a real singularity at the origin. Nearby orbits will separate from the orbit of at an average rate of , after k iterations of G.
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