Work

Topological and metric emergence of continuous maps

Year: 2024

Type: article

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.

Source: Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/s0305004124000343

Authors: MARIA CARVALHO, FAGNER B. RODRIGUES, PAULO VARANDAS

Institutions: Universidade do Porto, Centro de Matemática, Universidade Federal do Rio Grande do Sul

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funders: Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto