Hausdorff dimension of sets of generic points for non-statistical dynamical systems
Abstract We consider one-dimensional maps with several neutral fixed points that do not admit any physical measures. We show that there is a simplex of measures so that every measure in this simplex has a basin that has full Hausdorff dimension.
Authors
- Katrin Gelfert (ORCID: https://orcid.org/0000-0002-5123-4611)
- Douglas Coates (ORCID: https://orcid.org/0000-0003-3121-3335)
Institutions
- Universidade Federal do Rio de Janeiro (BR)
Publication Details
- Journal
- Ergodic Theory and Dynamical Systems
- Published
- 2026-04-30
- DOI
- https://doi.org/10.1017/etds.2026.10301
- 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
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro