Related papers: Hyperbolicity and Stability for Hamiltonian flows

We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed $3$-manifold (and more general Anosov-like actions) can be seen as an isometric action on a Gromov-hyperbolic space. When the flow is not $\R$-covered,…

We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…

The goal of this article is to establish several general properties of a somewhat large class of partially hyperbolic diffeomorphisms called \emph{discretized Anosov flows}. A general definition for these systems is presented and is proven…

We study cohomology of Holder continuous linear cocycles over a hyperbolic dynamical system and regularity of conjugacy between Anosov systems. For cocycles $A$ and $B$ with conjugate periodic data, we establish Holder cohomology under…

We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

We prove a radial source estimate in H\"older-Zygmund spaces for uniformly hyperbolic dynamics (also known as Anosov flows), in the spirit of Dyatlov-Zworski. The main consequence is a new linear stability estimate for the marked length…

Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…

We apply the matching functions technique in the setting of contact Anosov flows which satisfy a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman-Ornstein~\cite{FO}. Namely, we show that if two…

In this text we (re)-tell the theory of pseudo-Anosov flows on 3-manifolds with the orbit space as the central character; via a streamlined framework called {\em Anosov-like group actions}. This brings a simplified and unified perspective,…

We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the…

We are motivated by a conjecture of A. and S. Katok to study the smooth cohomologies of a family of Weyl chamber flows. The conjecture is a natural generalization of the Livshitz Theorem to Anosov actions by higher-rank abelian groups; it…

We consider dynamical stability for a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics. Our focus is on homogeneous metrics on non-compact manifolds. Following the program of Guenther,…

First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numerically observed as one type of metastable states in the study…

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the…

In this paper we establish conditions on the length of the second fundamental form of a complete minimal submanifold $M^n$ in the hyperbolic space $\mathbb{H}^{n+m}$ in order to show that $M^n$ is totally geodesic. We also obtain sharp…

Let $P$ be a principal U(1)-bundle over a closed manifold $M$. On $P$, one can define a modified version of the Ricci flow called the Ricci Yang-Mills flow, due to these equations being a coupling of Ricci flow and the Yang-Mills heat flow.…

We give a sufficient condition for the abstract basin of attraction of a sequence of holomorphic self-maps of balls in \mathbb{C}^{d} to be biholomorphic to \mathbb{C}^{d}. As a consequence, we get a sufficient condition for the stable…

In a recent paper, Chen, Erchenko and Gogolev have proven that if a Riemannian manifold with boundary has hyperbolic geodesic trapped set, then it can be embedded into a compact manifold whose geodesic flow is Anosov. They have to introduce…

We prove that homological stability holds for configuration spaces of orbifolds. This builds on the work of Bailes' thesis where he proves that the stabilisation maps are injective.