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An undecidable problem in dynamics

  • Jason Bell
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Abstract

Given a variety X with a self-map ϕ and subvarieties Y and Z of X, we consider the set of n for which ϕn(Y) intersects Z nontrivially. Extending a beautiful construction of Lee and Nam, we show this gives rise to an undecidable problem for a fixed ambient variety X and morphism ϕ. We further use this construction to give a counterexample to a conjecture of the author, Satriano, and Sierra.

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Cite

BibTeXRIS
BibTeX
@misc{bell2026undecidable,
  title = {{An undecidable problem in dynamics}},
  author = {Jason Bell},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22123},
  eprint = {2610.22123},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22123},
}
RIS
TY  - UNPB
TI  - An undecidable problem in dynamics
AU  - Jason Bell
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22123
UR  - https://arxiv.org/abs/2610.22123
AB  - Given a variety X with a self-map ϕ and subvarieties Y and Z of X, we consider the set of n for which ϕ^n(Y) intersects Z nontrivially. Extending a beautiful construction of Lee and Nam, we show this gives rise to an undecidable problem for a fixed ambient variety X and morphism ϕ. We further use this construction to give a counterexample to a conjecture of the author, Satriano, and Sierra.
ER  -