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PreprintCC BY-NC-ND 4.0arXiv

On the dynamics of self-consistent transfer operators for interval maps with singularities

  • Shadiyar Y. Altynbekov
  • Umrbek Olimov
  • Marks Ruziboev
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Abstract

We study the dynamics of self-consistent transfer operators associated with mean-field coupled systems whose unit dynamics is given by an interval map with finitely many singularities of cusp type. We show that, when the coupling strength is sufficiently weak, such an operator has a unique fixed point in a suitable cone of the associated Banach space, and that this fixed point attracts the orbit of every density in the cone at an exponential rate in the corresponding norm.

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Cite

BibTeXRIS
BibTeX
@misc{altynbekov2026dynamics,
  title = {{On the dynamics of self-consistent transfer operators for interval maps with singularities}},
  author = {Shadiyar Y. Altynbekov and Umrbek Olimov and Marks Ruziboev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10119},
  eprint = {2609.10119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10119},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the dynamics of self-consistent transfer operators for interval maps with singularities
AU  - Shadiyar Y. Altynbekov
AU  - Umrbek Olimov
AU  - Marks Ruziboev
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10119
UR  - https://arxiv.org/abs/2609.10119
AB  - We study the dynamics of self-consistent transfer operators associated with mean-field coupled systems whose unit dynamics is given by an interval map with finitely many singularities of cusp type. We show that, when the coupling strength is sufficiently weak, such an operator has a unique fixed point in a suitable cone of the associated Banach space, and that this fixed point attracts the orbit of every density in the cone at an exponential rate in the corresponding norm.
ER  -