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PreprintCC BY 4.0arXiv

Homological reduction and entropy of discontinuous interval maps

  • Henrique M. Oliveira
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Abstract

We develop a homological approach to the topological entropy of discontinuous interval maps with arbitrary branch orientations. Relations among the one-sided images of discontinuities reduce the kneading determinant, while symmetries yield further simplifications. We determine the smallest possible dimension of this reduction for each orientation pattern and show that this minimum can coexist with maximal entropy. The general theory is applied to maps with increasing or decreasing branches, extending earlier results for bimodal maps and yielding exact formulas for entropy and periodic-orbit counts.

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Cite

BibTeXRIS
BibTeX
@misc{oliveira2026homological,
  title = {{Homological reduction and entropy of discontinuous interval maps}},
  author = {Henrique M. Oliveira},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03287},
  eprint = {2611.03287},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03287},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Homological reduction and entropy of discontinuous interval maps
AU  - Henrique M. Oliveira
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03287
UR  - https://arxiv.org/abs/2611.03287
AB  - We develop a homological approach to the topological entropy of discontinuous interval maps with arbitrary branch orientations. Relations among the one-sided images of discontinuities reduce the kneading determinant, while symmetries yield further simplifications. We determine the smallest possible dimension of this reduction for each orientation pattern and show that this minimum can coexist with maximal entropy. The general theory is applied to maps with increasing or decreasing branches, extending earlier results for bimodal maps and yielding exact formulas for entropy and periodic-orbit counts.
ER  -