Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 30 min ago
PreprintCC BY 4.0arXiv

Linear-fractional rotational interval exchange transformations

  • Alexey Teplinsky
Open at sourcePDFDOICite

Abstract

Linear-fractional rotational interval exchange transformations appear naturally when investigating circle diffeomorphisms with breaks using the renormalization group approach. Earlier, we achieved an important rigidity result on circle diffeomorphisms with a single break by means of establishing a time-reversing duality for the corresponding commuting pairs of linear-fractional maps. In this paper, we extend the established duality to the case of multiple breaks, where a commuting pair from the previous case is replaced by a `commuting collection' of an even number of linear-fractional maps, which act according to a rotational interval exchange scheme of special type, while satisfying certain commutation relations.

Related

  1. Renormalization and rigidity of analytic non-linear interval exchange transformations
    Nataliya Goncharuk, Igors Gorbovickis, Michael Yampolsky
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  2. ALMOST EVERY PAIR OF INTERVAL EXCHANGE TRANSFORMATIONS DOES NOT GENERATE A FREE GROUP
    Sébastien Gouëzel
    HALPreprintCC BY 4.0Full textDynamical systemsHALarXiv
  3. Eigenvalues and eigenfunctions of the fractional Laplacian on the interval
    Cheng Zhang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsMathematical physicsarXiv
  4. Linear transformations of tropical matrices preserving individual values of the cyclicity index
    Alexander Guterman, Alexander Vlasov, Svetlana Zhilina
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. Weighted boundedness of maximal operator associated with invertible linear transformations on variable Lebesgue spaces
    Gonzalo H. Ibañez Firnkorn, Lucas A. Vallejos
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{teplinsky2026linearfractional,
  title = {{Linear-fractional rotational interval exchange transformations}},
  author = {Alexey Teplinsky},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40261},
  eprint = {2609.40261},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40261},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Linear-fractional rotational interval exchange transformations
AU  - Alexey Teplinsky
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40261
UR  - https://arxiv.org/abs/2609.40261
AB  - Linear-fractional rotational interval exchange transformations appear naturally when investigating circle diffeomorphisms with breaks using the renormalization group approach. Earlier, we achieved an important rigidity result on circle diffeomorphisms with a single break by means of establishing a time-reversing duality for the corresponding commuting pairs of linear-fractional maps. In this paper, we extend the established duality to the case of multiple breaks, where a commuting pair from the previous case is replaced by a `commuting collection' of an even number of linear-fractional maps, which act according to a rotational interval exchange scheme of special type, while satisfying certain commutation relations.
ER  -