English

Solvable subgroup theorem, length function and topological entropy

Dynamical Systems 2023-05-10 v1

Abstract

We prove a general solvable subgroup theorem in terms of length functions. As applications, we obtain a solvable subgroup theorem in dynamical systems: any solvable group of finite Hirsch length acting on a smooth manifold with uniformly positive topological entropies must be virtually Zn\mathbb{Z}^n.

Keywords

Cite

@article{arxiv.2305.05131,
  title  = {Solvable subgroup theorem, length function and topological entropy},
  author = {Shengkui Ye},
  journal= {arXiv preprint arXiv:2305.05131},
  year   = {2023}
}

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R2 v1 2026-06-28T10:29:19.172Z