Related papers: Transitive partially hyperbolic diffeomorphisms wi…
We consider a $C^1$ neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for…
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…
The purpose of this article is to obtain dynamically coherence of partially hyperbolic diffeomorphisms in certain classes of Anosov diffeomorphisms on nilmanifolds, extending a result due to T. Fisher, R. Potrie and M. Sambarino [FPS] on…
In this paper, we construct a partially hyperbolic skew-product diffeomorphism $f$ on $\mathbb{T}^3$, such that $f$ is accessible and chain transitive, but not transitive.
In this work, we study ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior, the main feature is a condition of transversality between unstable leaves when projected by the stable…
We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…
In [Discrete Contin. Dyn. Syst. \textbf{15} (2006), no. 3, 811--818.] Xia introduced a simple dynamical density basis for partially hyperbolic sets of volume preserving diffeomorphisms. We apply the density basis to the study of the…
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…
Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent…
We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphism in hyperbolic 3-manifolds as well as…
We study conservative partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds. We show that they are always accessible and deduce as a result that every conservative $C^{1+}$ partially hyperbolic in a hyperbolic 3-manifold must be…
This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and $ C^k $ normal forms for these objects are proved. Then, the theorems are applied to give…
We study perturbations of a partially hyperbolic toral automorphism L which is diagonalizable over C and has a dense center foliation. For a small perturbation of L with a smooth center foliation we establish existence of a smooth leaf…
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…
In this paper, we provide an example of a partially hyperbolic diffeomorphism with any finite number of physical measures when some Lyapunov exponent is 0 on the center.
Let $f$ be a $C^2$ partially hyperbolic diffeomorphisms of ${\mathbb T}^3$ (not necessarily volume preserving or transitive) isotopic to a linear Anosov diffeomorphism $A$ with eigenvalues $$\lambda_{s}<1<\lambda_{c}<\lambda_{u}.$$ Under…
In this paper we construct some "pathological" volume preserving partially hyperbolic diffeomorphisms on $\toro{3}$ such that their behaviour in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their…
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…
We consider partially hyperbolic \( C^{1+} \) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \( E^s\oplus E^{cu} \). Assuming the existence of a set of…