Download Conditional Stability and Real Analytic Pseudo-Anosov Maps by Marlies Gerber PDF

By Marlies Gerber

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15. 10. 13a) // P r 2 \ 2 / P a 1 \ s = mini 1 2 k\i » 9A*/ Let x €

P-l? where (g^) small then such a curve ( "^ifx* x. 5. Proof. 7) Let a / P h a k > 2, |s 2' leaves where (Note that e = e(k,p) with P. Moreover, sufficiently lies in until )' p = p(i). (P )"1{(s ,s ): i i 1 2 g Let x g~n and ordinate system by x by the properties of |s2l > 2 S l }. ,a9) g~ and (aJ,a£), (s. ,s^) co- respectively. 3, a ! 1 a _ <~» 2XVk > ancJ A i / i . 2b) hold with — ^ ~ a z L ax2 — 2XVk n(x) = n(x) and k I! "^ II replaced by 2Vk. ,n(x) occurs if £ = n(x) , a = a 0 and a J = l , l L 1 \V2 »%2 /(ai>2 + (a') ai = XV2 a 0 .

In the C There exist a neighborhood topology and eQ > 0 m Wn of g such that if /. ,x } the intersections , h = n dh n K + „ n>0 h'nx and Es . x h > = are one-dimensional subspaces of Clearly, such line fields Jy invariant. T M. 1, stable and unstable curves are defined as in §4. 2). ,x } to be slopes with respect to the 1 m (£,,£9> coordinate systems defined in §5. If we do not restrict to a single S? , i > m, or a single these coordinates are only defined up to changes of sign in each of the coordinates.

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