arXiv subjects

Marcielis Espitia

Publications and source records attributed to Marcielis Espitia.

3 recordsLinked to original sources

arXiv2025

Homoclinic classes for flows: ergodicity and SRB measures

In this work we intend to study homoclinic classes for some classes of flows. To this end we obtain analogous results those obtained by Hertz-Hertz-Tahzibi-Ures in the flow setting. Namely we prove that if the Lesbegue measure gives positive measure to both stable and unstable homoclinic classes of a periodic hyperbolic orbit, then their intersection constitute an ergodic component. Futhermore, with similar techiniques we state several results concerning regular SRB measures.

math.DS↗

arXiv2025

Classification of Conditional Measures Along Certain Invariant One-Dimensional Foliations

Let $f:M\to M$ be a homeomorphism over a compact Riemannian manifold, ergodic with respect to a measure $μ$ defined on the completion of the Borel $σ$-algebra and $\mathcal F$ a $f$-invariant one dimensional continuous foliation of $M$ by $C^1$-leaves. Then, if $f$ preserves a continuous $\mathcal{F}$-arc length system, then we only have three possibilities for the conditional measures of $μ$ along $\mathcal F$, namely: - they are atomic for almost every leaf, or - for almost every leaf they are equivalent to the measure $λ_x$ induced by the invariant arc-length system over $\mathcal F$, or - for almost every leaf their support is a nowhere dense, perfect subset of the leaf. Furthermore, we show that restricted to ergodic partially hyperbolic diffeomorphism with one-dimensional topological neutral center direction, we are able to eliminate the third case obtaining a dichotomy.

math.DS↗

arXiv2024

Quasi-isometric center action in dimension 3

We study transitive partially hyperbolic diffeomorphisms in dimension 3 preserving a center foliation on which they act quasi-isometrically. We show that the diffeomorphism is up to finite lift and iterate, either a skew-product or a discretised Anosov flow.

math.DS↗