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An earthquake is roughly a sort of limit of simple earthquakes, where one has an infinite number of geodesics, and instead of attaching a positive real number to each geodesic one puts a measure on them.
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More generally one can do the same construction with a finite number of disjoint simple geodesics, each with a real number attached to it. The result is called a simple earthquake.
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consists of a map between copies of the hyperbolic plane with geodesic laminations, that is an isometry from each stratum of the foliation to a stratum. Moreover, if
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to the left, and glue them back. This gives a new hyperbolic surface, and the (possibly discontinuous) map between them is an example of a left earthquake.
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289:(1986), "Earthquakes in two-dimensional hyperbolic geometry", in D.B.A. Epstein (ed.),
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of a hyperbolic surface is a closed subset with a foliation by geodesics. A
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Thurston's earthquake theorem states that for any two points
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is the isometry of the whole plane that restricts to
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is a hyperbolic transformation whose axis separates
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on an oriented hyperbolic surface and a real number
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291:Low dimensional topology and Kleinian groups
199:(1983), "The Nielsen realization problem",
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129:and which translates to the left, where
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170:there is a unique left earthquake from
19:For maps of literal earthquakes, see
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257:Travaux de Thurston sur les surfaces
260:, Astérisque, vol. 66, Paris:
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262:Société Mathématique de France
16:Concept in hyperbolic geometry
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38:into another, introduced by
34:is a method of changing one
184:Nielsen realization problem
182:, who used it to solve the
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295:Cambridge University Press
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326:Functions and mappings
202:Annals of Mathematics
287:Thurston, William P.
197:Kerckhoff, Steven P.
98:are two strata then
40:William Thurston
321:Hyperbolic geometry
146:, and likewise for
81:geodesic lamination
36:hyperbolic manifold
28:hyperbolic geometry
154:Earthquake theorem
21:Seismic hazard map
304:978-0-521-33905-6
271:978-99920-1-230-7
205:, Second Series,
168:Teichmüller space
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54:Given a
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144:A
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131:E
127:B
123:A
117:B
111:E
106:A
100:E
96:B
92:A
88:E
67:t
63:t
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