Hausdorff measures for dissipative Poincaré maps of Cherry flows
Cherry flows in general have quasi-minimal sets whose cross sections are Cantor sets. If their return maps, also called gap maps, have derivative smaller than one, then they are very tiny, in the sense that they have null Hausdorff dimension. We then resorted to a more general definition of dimension proposed by Felix Hausdorff in his original paper to understand the sizes of these sets under an appropriate lens.
Authors
- Márcio R. A. Gouveia (ORCID: https://orcid.org/0000-0003-0891-9372)
- Eduardo Colli (ORCID: https://orcid.org/0000-0003-2167-8542)
Institutions
- Universidade Estadual Paulista (Unesp) (BR)
Publication Details
- Journal
- Discrete and Continuous Dynamical Systems
- Published
- 2025-01-01
- DOI
- https://doi.org/10.3934/dcds.2025111
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Division of Graduate Education