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

Institutions

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

Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Partially hyperbolic geodesic flow via conformal deformation

Sergio Romaña, Luis Pedro Piñeyrúa, Ygor de Jesus
Advances in Mathematics
Mathematical Dynamics and Fractals
article

Partially hyperbolic geodesic flow via conformal deformation

Sergio Romaña, Luis Pedro Piñeyrúa, Ygor de Jesus
article en

Abstract

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.

Advances in MathematicsVol. 505
Sun Yat-sen University (CN), Universidad de la República de Uruguay (UY)
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
Openalex Percentile: Top 92%
Mathematical Dynamics and Fractals
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.