Homeomorphisms of S1and Factorization

Mark Dalthorp, Doug Pickrell

Research output: Contribution to journalArticlepeer-review


For each n>0 there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations "conjugated by z \to zn. We show that these families are free of relations, which determines the structure of "the group of homeomorphisms of finite type". We next consider factorization for more robust groups of homeomorphisms. We refer to this as root subgroup factorization (because the factors correspond to root subgroups). We are especially interested in how root subgroup factorization is related to triangular factorization (i.e., conformal welding) and correspondences between smoothness properties of the homeomorphisms and decay properties of the root subgroup parameters. This leads to interesting comparisons with Fourier series and the theory of Verblunsky coefficients.

Original languageEnglish (US)
Pages (from-to)16859-16909
Number of pages51
JournalInternational Mathematics Research Notices
Issue number22
StatePublished - Nov 1 2021

ASJC Scopus subject areas

  • General Mathematics


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