Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full families of generalized interval exchange transformations   We consider generalized interval exchange transformations, or briefly GIETs,
that is bijections of the interval which are piecewise increasing
homeomorphisms with finite branches. When all continuous branches are
translations, such maps are classical interval exchange transformations, or
briefly IETs. The well-known Rauzy renormalization procedure extends to a given
GIET and a Rauzy renormalization path is defined, provided that the map is
infinitely renormalizable. We define full families of GIETs, that is optimal
finite dimensional parameter families of GIETs such that any prescribed Rauzy
renormalization path is realized by some map in the family. In particular, a
GIET and a IET with the same Rauzy renormalization path are semi-conjugated.
This extends a classical result of Poincar\'e relating circle homeomorphisms
and irrational rotations.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: econ