2024/10/28 by Ygor de Jesus, Luis Pedro Piñeyrúa, de Jesus, Ygor +3
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2410.21519
This paper presents a new construction of non-Anosov Partially Hyperbolic Geodesic flows. Our construction is closely related to the construction made by Carneiro and Pujals, 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. Besides that, we could 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 finner 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 to also produce metrics with partially hyperbolic geodesic flows and conjugate points.