arXiv subjects

Mounib Abouanass

Publications and source records attributed to Mounib Abouanass.

4 recordsLinked to original sources

arXiv2026

On transversely holomorphic partially hyperbolic flows

In this paper, we study transversely holomorphic partially hyperbolic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove in the seven-dimensional case that under the assumption that the subcenter distribution is integrable to a flow invariant compact foliation with trivial holonomy, then the flow projects, by a smooth fiber bundle map, to a transversely holomorphic Anosov flow on a smooth five-dimensional manifold which is, in case of topological transitivity, either $C^\infty$ orbit equivalent to the suspension of a hyperbolic automorphism of a complex torus, or, up to finite covers, $C^\infty$-orbit equivalent to the geodesic flow of a compact hyperbolic manifold.

math.DS↗

arXiv2026

On global rigidity of transversely holomorphic Anosov flows

In this paper, we study transversely holomorphic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove that for Anosov flows on smooth compact manifolds, the strong unstable (respectively, stable) distribution is integrable to complex manifolds, on which the flow acts holomorphically. Furthermore, assuming its complex dimension to be one, it is uniquely integrable to complex affine one-dimensional manifolds, each moreover affinely diffeomorphic to $\mathbb C$, on which the flow acts affinely. In this case, the weak stable (respectively, unstable) foliation is transversely holomorphic, and even transversely projective if the flow is assumed to be topologically transitive. By combining these facts in low dimensions, our main result is as follows : if a transversely holomorphic Anosov flow on a smooth compact five-dimensional manifold is topologically transitive, then it is either $C^\infty$-orbit equivalent to the suspension of a hyperbolic automorphism of a complex torus, or, up to finite covers, $C^\infty$-orbit equivalent to the geodesic flow of a compact hyperbolic manifold.

math.DS↗

arXiv2026

Versal deformation of transversely holomorphic flows on the boundary of strongly convex domains of $\mathbb C^n$

In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $ξ$ defined on a neighborhood of the closure of a bounded strongly convex open domain $Ω\subset\mathbb C^n$ ($n\geq2$) with smooth boundary, with its boundary $\partial Ω$. That is, any germ of deformation of $\mathcal{F}_0$ is also obtained by intersecting the orbits of a deformation of $ξ$ with the boundary of $Ω$.

math.CV↗

arXiv2026

On dynamical coherence of partially hyperbolic flows

In this paper, we introduce the notion of dynamical coherence for a partially hyperbolic flow $(φ^t)$ on a smooth compact manifold $M$, and prove it under the assumption that there exists a compact foliation with trivial holonomy which integrates the subcenter distribution.

math.DS↗