Topological and metric emergence of continuous maps
Dynamical Systems
2025-01-08 v2
Abstract
We prove that the homeomorphisms of a compact manifold with dimension one have zero topological emergence, whereas in dimension greater than one the topological emergence of a C^0-generic conservative homeomorphism is maximal, equal to the dimension of the manifold. Moreover, we show that the metric emergence of continuous self-maps on compact metric spaces has the intermediate value property.
Keywords
Cite
@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}
}
Comments
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