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PreprintCC0arXiv

Open dynamical systems in topologically expansive decreasing Lorenz maps

  • Yiming Ding
  • Wolfgang Steiner
  • Yun Sun
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Abstract

We develop a parity-sensitive admissibility theory for topologically expansive decreasing Lorenz maps. By embedding them into the standard circle map m−2, we realize every decreasing-admissible pair. We then study the negative doubling map T−2 with a hole (a,b), where 0<a≤1/2≤ b<1. Using the alternating lexicographic order, we classify plateaux of the symbolic survivor spaces. Under weak admissibility and strict shifted ordering, the boundary subshifts are realized as kneading spaces of decreasing Lorenz maps. We also establish entropy correspondences across countable itinerary discrepancies in completed survivor systems. For fixed a, we prove that b↦dimHS−2(a,b) is a devil's staircase, possibly constant. Under the pullback-null condition~(P), we obtain the corresponding survivor-entropy result for expansive decreasing Lorenz maps. We verify this condition for the piecewise-linear family in Example 5.1.

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Cite

BibTeXRIS
BibTeX
@misc{ding2026open,
  title = {{Open dynamical systems in topologically expansive decreasing Lorenz maps}},
  author = {Yiming Ding and Wolfgang Steiner and Yun Sun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03327},
  eprint = {2610.03327},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03327},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Open dynamical systems in topologically expansive decreasing Lorenz maps
AU  - Yiming Ding
AU  - Wolfgang Steiner
AU  - Yun Sun
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03327
UR  - https://arxiv.org/abs/2610.03327
AB  - We develop a parity-sensitive admissibility theory for topologically expansive decreasing Lorenz maps. By embedding them into the standard circle map m_−2, we realize every decreasing-admissible pair. We then study the negative doubling map T_−2 with a hole (a,b), where 0<a≤1/2≤ b<1. Using the alternating lexicographic order, we classify plateaux of the symbolic survivor spaces. Under weak admissibility and strict shifted ordering, the boundary subshifts are realized as kneading spaces of decreasing Lorenz maps. We also establish entropy correspondences across countable itinerary discrepancies in completed survivor systems. For fixed a, we prove that b↦dim_HS_−2(a,b) is a devil's staircase, possibly constant. Under the pullback-null condition~(P), we obtain the corresponding survivor-entropy result for expansive decreasing Lorenz maps. We verify this condition for the piecewise-linear family in Example 5.1.
ER  -