Topological and metric emergence of continuous maps
Abstract We prove that every homeomorphism of a compact manifold with dimension one has zero topological emergence, whereas in dimension greater than one the topological emergence of a $C^0-$ generic homeomorphism is maximal, equal to the dimension of the manifold. We also show that the metric emergence of a continuous self-map on compact metric space has the intermediate value property.
Authors
- Paulo Varandas (ORCID: https://orcid.org/0000-0002-0902-8718)
- Fagner B. Rodrigues (ORCID: https://orcid.org/0000-0002-7596-8214)
- Maria Carvalho (ORCID: https://orcid.org/0000-0001-6929-6442)
Institutions
- Universidade Federal do Rio Grande do Sul (BR)
- Universidade do Porto (PT)
Publication Details
- Journal
- Mathematical Proceedings of the Cambridge Philosophical Society
- Published
- 2024-11-01
- DOI
- https://doi.org/10.1017/s0305004124000343
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fundação para a Ciência e a Tecnologia
- Centro de Matemática Universidade do Porto