## Nielsen-Thurston reducibility and renormalization

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- by Olivier Courcelle, Jean-Marc Gambaudo and Charles Tresser
- Proc. Amer. Math. Soc.
**125**(1997), 3051-3058 - DOI: https://doi.org/10.1090/S0002-9939-97-04159-2
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## Abstract:

Consider an orientation preserving homeomorphism $f$ of the 2-disk with an infinite set of nested periodic orbits $\{\mathcal {O}_n\}_{n\ge 1}$, such that, for all $m>1$, the restriction of $f$ to the complement of the first $m$ orbits, from $\mathcal {O}_1$ to $\mathcal {O}_m$, is $m-1$ times reducible in the sense of Nielsen and Thurston. We define combinatorial renormalization operators for such maps, and study the fixed points of these operators. We also recall the corresponding theory for endomorphisms of the interval, and give elements of comparison of the theories in one and two dimensions.## References

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## Bibliographic Information

**Olivier Courcelle**- Affiliation: Section de Mathématiques, Université de Genève, CP240, CH1211 Genève 24, Suisse
- Email: courcell@divsun.unige.ch
**Jean-Marc Gambaudo**- Affiliation: INLN, 1361 route des lucioles, Sophia-Antipolis, 06560 Valbonne, France
- Email: jmga@ecu.unice.fr
**Charles Tresser**- Affiliation: IBM, P.O. Box 218, Yorktown Heights, New York 10598
- MR Author ID: 174225
- Email: tresser@watson.ibm.com
- Received by editor(s): October 24, 1995
- Communicated by: Linda Keen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 3051-3058 - MSC (1991): Primary 58F99
- DOI: https://doi.org/10.1090/S0002-9939-97-04159-2
- MathSciNet review: 1425117