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Distributional Chaos in Over-Saturated Sets

  • Chenwei Yu
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Abstract

We study distributional chaos in over-saturated sets under the non-uniform specification property. We prove that for any dynamical system with the non-uniform specification property, every non-empty over-saturated set exhibits distributional chaos of type 1. We further provide sufficient conditions for certain differences of over-saturated sets to exhibit distributional chaos of type 1. We also construct examples showing that some of these conditions are optimal.

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Cite

BibTeXRIS
BibTeX
@misc{yu2026distributional,
  title = {{Distributional Chaos in Over-Saturated Sets}},
  author = {Chenwei Yu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14547},
  eprint = {2609.14547},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14547},
}
RIS
TY  - UNPB
TI  - Distributional Chaos in Over-Saturated Sets
AU  - Chenwei Yu
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14547
UR  - https://arxiv.org/abs/2609.14547
AB  - We study distributional chaos in over-saturated sets under the non-uniform specification property. We prove that for any dynamical system with the non-uniform specification property, every non-empty over-saturated set exhibits distributional chaos of type 1. We further provide sufficient conditions for certain differences of over-saturated sets to exhibit distributional chaos of type 1. We also construct examples showing that some of these conditions are optimal.
ER  -