Topological and metric emergence of continuous maps

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.

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

References in corpus (2)

• Emergence via non-existence of averages
• Invariant measures for typical continuous maps on manifolds