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Full Topological entropy of Xiong chaotic sets beyond the specification property

  • Xinyun Zhang
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Abstract

In this paper, we show that for a shift dynamical system (Xℒ, σ) with a weakened form of the specification property, there exists a Xiong chaotic set C of Xℒ with full topological entropy everywhere (i.e. the intersection of C and arbitrary non-empty open subset of Xℒ has full topological entropy). Moreover, C satisfies that for any non-empty subset A and any continuous map F: A→ Xℒ, there exists an increasing sequence {pk}k=1+∞ of positive integers such that limk→ +∞σpk(x)=F(x) holds for any x∈ A.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026full,
  title = {{Full Topological entropy of Xiong chaotic sets beyond the specification property}},
  author = {Xinyun Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.29171},
  eprint = {2608.29171},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29171},
}
RIS
TY  - UNPB
TI  - Full Topological entropy of Xiong chaotic sets beyond the specification property
AU  - Xinyun Zhang
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2608.29171
UR  - https://arxiv.org/abs/2608.29171
AB  - In this paper, we show that for a shift dynamical system (X_ℒ, σ) with a weakened form of the specification property, there exists a Xiong chaotic set C of X_ℒ with full topological entropy everywhere (i.e. the intersection of C and arbitrary non-empty open subset of X_ℒ has full topological entropy). Moreover, C satisfies that for any non-empty subset A and any continuous map F: A→ X_ℒ, there exists an increasing sequence {p_k}_k=1^+∞ of positive integers such that lim_k→ +∞σ^p_k(x)=F(x) holds for any x∈ A.
ER  -