Related papers: Robust Transitivity of Partially Hyperbolic Diffeo…
In the present paper we contribute to the thermodynamic formalism of partially hyperbolic attractors for local diffeomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a…
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)…
We show stable ergodicity of a class of conservative diffeomorphisms which do not have any hyperbolic invariant subbundle. Moreover the uniqueness of SRB measures for non-conservative $C^1$ perturbations of such diffeomorphisms. This class…
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…
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…
This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…
It was shown that in robustly transitive, partially hyperbolic diffeomorphisms on three dimensional closed manifolds, the strong stable or unstable foliation is minimal. In this article, we prove ``almost all'' leaves of both stable and…
In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center segments remains small. Such systems are dynamically coherent.…
In this paper we improve the results of \cite{MT} and show that a weak hyperbolic transitivity implies the uniqueness of hyperbolic SRB measures. As an important corollary, it arises the ergodicity of the system in a conservative setting.…
It is well-known that it is possible to construct a partially hyperbolic diffeomorphism on the 3-torus in a similar way than in Kan's example. It has two hyperbolic physical measures with intermingled basins supported on two embedded tori…
We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to characterise the dynamics in the presence of periodic centre…
A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions it is known to have a unique…
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 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…
We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an…
We prove that every dynamically coherent plaque expansive partially hyperbolic diffeomorphism is topologically stable with respect to the central foliation (in short, {\em plaque topologically stable}). Next, we study partially hyperbolic…
In this work, we deal with a notion of partially hyperbolic endomorphism. We explore topological properties of this definition and we obtain, among other results, obstructions to get center leaf conjugacy with the linear part, for a class…
We prove the stochastic stability of an open class of partially hyperbolic diffeomorphisms, each of which admits two centers $E^c_1$ and $E^c_2$ such that any Gibbs $u$-state admits only positive (resp. negative) Lyapunov exponents along…
We show that for $n\ge2$, if a partially hyperbolic diffeomorphism $f:\mathbb T^{n+1}\to \mathbb T^{n+1}$ with $\dim E^s=\dim E^c=1$ has an invariant center-unstable foliation with a compact incompressible leaf, then this foliation has a…
We prove, for f a partially hyperbolic diffeomorphism with center dimension one, two results about the integrability of its central bundle. On one side, we show that if the non wandering set of f is the whole manifold, and the manifold is 3…