English

Anomalous cw-expansive homeomorphisms on compact surfaces of higher genus

Dynamical Systems 2026-01-01 v1

Abstract

In this paper, we construct cw-expansive homeomorphisms on compact surfaces of genus greater than or equal to zero with a fixed point whose local stable set is connected but not locally connected. This provides an affirmative answer to question posed by Artigue [3]. To achieve this, we generalize the construction from the example of Artigue, Pacifico and Vieitez [6], obtaining examples of homeomorphisms on compact surfaces of genus greater than or equal to two that are 2-expansive but not expansive. On the sphere and the torus, we construct new examples of cw2-expansive homeomorphisms that are not N -expansive for all N greater than or equal to one.

Keywords

Cite

@article{arxiv.2512.24904,
  title  = {Anomalous cw-expansive homeomorphisms on compact surfaces of higher genus},
  author = {Alberto Sarmiento and Douglas Danton and Viviane Pardini Valério},
  journal= {arXiv preprint arXiv:2512.24904},
  year   = {2026}
}

Comments

13 pages, 6 figures