连续映射的拓扑与度量涌现
动力系统
2025-01-08 v2
摘要
我们证明了一维紧致流形上的同胚具有零拓扑涌现，而在大于一维时，C^0通有保守同胚的拓扑涌现达到最大，等于流形的维数。此外，我们证明了紧致度量空间上连续自映射的度量涌现具有介值性质。
引用
@article{arxiv.2208.00962,
title = {Topological and metric emergence of continuous maps},
author = {Maria Carvalho and Fagner B. Rodrigues and Paulo Varandas},
journal= {arXiv preprint arXiv:2208.00962},
year = {2025}
}
备注
Now the paper also contains results about generic dissipative homeomorphisms on dimension greater than two and an application about the metric order of the space of pseudo-physical measures of C^0-generic homeomorphisms