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Linearization of generalized interval exchange maps
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DOI：10.4007/annals.2012.176.3.5.png)
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A standard interval exchange map is a one-to-one map of the interval which is locally a translation except at finitely many singularities. We define for such maps, in terms of the Rauzy-Veech continuous fraction algorithm, a diophantine arithmetical condition called restricted Roth type which is almost surely satisfied in parameter space. Let T-0 be a standard interval exchange map of restricted Roth type, and let r be an integer >= 2. We prove that, amongst Cr+3 deformations of T-0 which are Cr+3 tangent to T-0 at the singularities, those which are conjugated to T-0 by a C-r diffeomorphism close to the identity form a C-1 submanifold of codimension (g - 1) (2r + 1) + s. Here, g is the genus and s is the number of marked points of the translation surface obtained by suspension of T-0. Both g and s can be computed from the combinatorics of T-0.
Keyword:
AREA-PRESERVING FLOWS
AFFINE INTERVAL
COHOMOLOGICAL EQUATION
METRIC THEORY
TRANSFORMATIONS
SPACE
DEVIATION
SURFACES
DECAY
期刊
IF:
5.3
论文数:
1.4K
被引数:
1.6W
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