Related papers: A note on minimality of foliations for partially h…

We prove robustness and uniqueness of equilibrium states for a class of partially hyperbolic diffeomorphisms with dominated splittings and H\"older continuous potentials with not very large oscillation.

We study the topological properties of expanding invariant foliations of $C^{1+}$ diffeomorphisms, in the context of partially hyperbolic diffeomorphisms and laminations with $1$-dimensional center bundle. In this first version of the…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

We study 3-dimensional dynamically coherent partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the transverse geometry and topology of the center stable and center unstable foliations, and the dynamics…

We briefly survey some of the recent results concerning the metric behavior of the invariant foliations for a partially hyperbolic on a three-dimensional manifold and propose a conjecture to characterize atomic behavior for conservative…

Let M be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the M-isoperiodic foliation are either all closed or all dense. In the second case, we establish ergodicity of the…

We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a meager subset of the manifold.

We prove that any C1-stably weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E + F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result…

Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism.

The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…

In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that…

We prove that in the isotopy class of any volume preserving partially hyperbolic diffeomorphism in a $3$-dimensional manifold, there is a non-partially hyperbolic stably ergodic diffeomorphism. In particular, we provide new examples of…

We consider stable manifolds of a holomorphic diffeomorphism of a complex manifold. Using a conjugation of the dynamics to a (non-stationary) polynomial normal form, we show that typical stable manifolds are biholomorphic to complex…

We prove that a class of weakly partially hyperbolic endomorphisms on $\mathbb{T}^2$ are dynamically coherent and leaf conjugate to linear toral endomorphisms. Moreover, we give an example of a partially hyperbolic endomorphism on…

The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We…

We introduce a notion of autonomous dynamical systems and apply it to prove rigidity of partially hyperbolic diffeomorphisms on closed compact three-manifolds under some smoothness hypothesis of their associated framing.

Let $f: \mathbb{T}^3\to\mathbb{T}^3$ be a partially hyperbolic diffeomorphism on the 3-torus $\mathbb{T}^3$. In his thesis, Hammerlindl proved that for lifted center foliation $\mathcal{F}^c_f$, there exists $R>0$, such that for any $x\in…

We show that if an endomorphism $f:\mathbb{T}^2 \to \mathbb{T}^2$ is absolutely partially hyperbolic, then it has a center foliation. Moreover, the center foliation is leaf conjugate to that of its linearization.

We show that a partially hyperbolic $C^1$ -diffeomorphism $f : M \to M$ with a uniformly compact $f$ -invariant center foliation $F^c$ is dynamically coherent. Further, the induced homeomorphism $F : M/F^c \to M/F^c$ on the quotient space…