Solvable subgroup theorem, length function and topological entropy

Shengkui Ye

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arXiv · 2305.05131

Solvable subgroup theorem, length function and topological entropy

Shengkui Ye

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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 $\mathbb{Z}^n$.

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Shengkui Ye. 2023-05-09. Solvable subgroup theorem, length function and topological entropy. https://arxiv.org/abs/2305.05131

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