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Luis Pedro Piñeyrúa

Publications and source records attributed to Luis Pedro Piñeyrúa.

6 recordsLinked to original sources
arXiv2026

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 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.

math.DS↗
arXiv2026

Robust transitivity of geodesic flows from metrics with conjugate points

In this article, we prove a general criterion for obtaining robust transitivity of partially hyperbolic geodesic flows. As a consequence, we exhibit the first example of a $C^2$ open set of Riemannian metrics with conjugate points and transitive geodesic flow. In particular, such a set does not intersect the set of Riemannian metrics with Anosov geodesic flows.

math.DS↗
arXiv2025

Some hyperbolicity revisited and robust transitivity

In this article we revisit the notion of \textit{Some Hyperbolicity} introduced by Pujals and Sambarino in \cite{PuSa}. We present a more general definition, that in particular can be applied to the symplectic context (something that the previous couldn't). As an application we construct $C^1$ robustly transitive derived from Anosov diffeomorphisms with mixed behaviour on center leaves.

math.DS↗
arXiv2023

Dynamical coherence in isotopy classes of fibered lifted partially hyperbolic diffeomorphisms

We introduce the notion of \textit{fibered lifted partially hyperbolic diffeomorphisms} and we prove that any partially hyperbolic diifeomorphism isotopic to a fibered lifted one where the isotopy take place inside partially hyperbolic systems is \textit{dynamically coherent.} Moreover we prove some global stability result: every two partially hyperbolic diffeomorphisms in the same connected component of a fibered lifted partially hyperbolic diffeomorphisms, are leaf conjugate.

math.DS↗