Partially hyperbolic geodesic flow via conformal deformation
This paper presents a new construction of non-Anosov partially hyperbolic geodesic flows. Our construction is closely related to the construction presented in [10] , the novelty is the use of conformal deformations to produce the examples. Some of the necessary conditions appear more naturally and are easier to check. Moreover, we can enumerate the conditions required to produce partially hyperbolic geodesic flow examples. We show how to produce examples with metrics that are non-positively curved, and with a finer analysis we can prove ergodicity for the Liouville measure and uniqueness of the measure of maximal entropy. These examples lie on the boundary of Anosov metrics, allowing us also to produce metrics with partially hyperbolic geodesic flows and conjugate points.
Authors
- Sergio Romaña (ORCID: https://orcid.org/0000-0002-3253-0626)
- Luis Pedro Piñeyrúa
- Ygor de Jesus
Institutions
- Sun Yat-sen University (CN)
- Universidad de la República de Uruguay (UY)
Publication Details
- Journal
- Advances in Mathematics
- Published
- 2026-10-07
- DOI
- https://doi.org/10.1016/j.aim.2026.111308
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- University of Pennsylvania
- Pennsylvania State University
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- National Natural Science Foundation of China
- Southern University of Science and Technology
- Instituto Serrapilheira