9.1 Inversion

As was explained in Section 6.3, Equations (16View Equation) – (17View Equation) can be viewed as wave-map equations with hyperbolic space as a target. As a consequence, isometries of hyperbolic space map solutions to solutions. In the context of spikes, one isometry of (ℝ2, g ) R, which is particularly important (as was noted in [71Jump To The Next Citation Point]) is
[ ] Q0 2 −2P0 Inv(Q0, P0) = Q2-+--e−2P0,P0 + ln(Q0 + e ) . (40 ) 0
We shall refer to this isometry as an inversion; in the upper half plane, it corresponds to an inversion in the unit circle with center at the origin.
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