Related papers: Partially hyperbolic diffeomorphisms with a trappi…
For a boundary-preserving partially hyperbolic diffeomorphism with interval central leaves, we completely characterize the $C^k$-robust transitivity $(k\geq 2)$ by boundary interconnection. As an application, if the boundary SRB measures…
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially…
We derive some statistical properties for equilibrium states of partially hyperbolic horseshoes. We define a projection map associated to the horseshoe and prove a spectral gap for its transfer operator acting on the space of H\"older…
We develop a general geometric method to establish the existence of positive Lyapunov exponents for a class of skew products. The technique is applied to show non-uniform hyperbolicity of some conservative partially hyperbolic…
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…
We prove that divergent, extended geometrically finite (in the sense of Weisman arXiv:2205.07183) representations can be interpreted as restricted Anosov (in the sense of Tholozan--Wang arXiv:2307.02934) representations over certain flow…
We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also…
We study the behavior of hyperbolic affine automorphisms of a translation surface which is infinite in area and genus that is obtained as a limit of surfaces built from regular polygons studied by Veech. We find that hyperbolic affine…
We prove transitivity for volume preserving $C^{1+}$ diffeomorphisms on $\mathbb{T}^3$ which are isotopic to a linear Anosov automorphism along a path of weakly partially hyperbolic diffeomorphisms.
We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the…
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.
We study a class of two dimensional partially hyperbolic systems, not necessarily skew products, trying to establish the germ of a general theory. To illustrate the scope of the theory, we apply our results to the case of fast-slow…
We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $\mathbb{T}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along…
We propose a generalization of the concept of discretized Anosov flows that covers a wide class of partially hyperbolic diffeomorphisms in 3-manifolds, and that we call collapsed Anosov flows. They are related with Anosov flows via a self…
We study fractal properties of invariant graphs of hyperbolic and partially hyperbolic skew product diffeomorphisms in dimension three. We describe the critical (either Lipschitz or at all scales H\"older continuous) regularity of such…
We prove several rigidity results about the centralizer of a smooth diffeomorphism, concentrating on two families of examples: diffeomorphisms with transitive centralizer, and perturbations of isometric extensions of Anosov diffeomorphisms…
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…
We characterize and describe the extensions of expansive and Anosov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system…
Bochi-Katok-Rodriguez Hertz proposed in [BKH21] a program on the flexibility of Lyapunov exponents for conservative Anosov diffeomorphisms, and obtained partial results in this direction. For conservative Anosov diffeomorphisms with strong…
We show that time-one maps of transitive Anosov flows of compact manifolds are accumulated by diffeomorphisms robustly satisfying the following dichotomy: either all of the measures of maximal entropy are non-hyperbolic, or there are…