相关论文: Morse and Lyapunov Spectra and Dynamics on Flag Bu…

We prove differentiability of certain linear combinations of the Lyapunov spectra of a flow on a principal bundle of a semi-simple Lie group. The specific linear combinations that yield differentiability are determined by the finest Morse…

Consider a continuous flow of automorphisms of a G-principal bundle which is chain transitive on its compact Hausdorff base. Here G is a connected noncompact semi-simple Lie group with finite center. The finest Morse decomposition of the…

We introduce the \emph{metric spectrum}, which measures the exponential rate of approximation to an isolated invariant set of points starting in its stable set, and relate it to the Lyapunov spectrum. We determine the metric spectrum of…

The goal of the present work is to compute explicitely the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents of the Morse--Smale flow, the topology of the flow around periodic orbits and the monodromy of some…

Let $Q\rightarrow X$ be a continuous principal bundle whose group $G$ is reductive. A flow $\phi $ of automorphisms of $Q$ endowed with an ergodic probability measure on the compact base space $X$ induces two decompositions of the flag…

We consider families of diffeomorphisms with dominated splittings and preserving a Borel probability measure, and we study the regularity of the Lyapunov exponents associated to the invariant bundles with respect to the parameter. We obtain…

Let $G$ be a compact Lie group. We introduce a semiclassical framework, called Borel-Weil calculus, to investigate $G$-equivariant (pseudo)differential operators acting on $G$-principal bundles over closed manifolds. In this calculus, the…

We express the diagonals of projective, Grassmann and, more generally, flag bundles of type (A) using the zero schemes of some vector bundle sections, and do the same for their single point subschemes. We discuss diagonal and point…

We demonstrate that a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition identifies subspaces with stable Lyapunov exponents and allows the dynamics to exhibit properties of an…

On a smooth, compact and oriented manifold without boundary, we give a complete description of the correlation function of a Morse-Smale gradient flow satisfying a certain nonresonance assumption. This is done by analyzing precisely the…

We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the…

This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined…

We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are…

For a right-invariant control system on a flag manifold $\mathbb{F}_{\Theta}$ of a real semisimple Lie group, we relate the $\mathfrak{a}$-Lyapunov exponents to the Lyapunov exponents of the system over regular points. Moreover, we adapt…

An important aspect of Weyl anomalies is that they encode information on the irreversibility of the renormalisation group flow. We consider, $\Delta \bar b = \bar{b}^{\textrm{UV}} - \bar{b}^{\textrm{IR}}$, the difference of the ultraviolet…

In the following article we study the limiting properties of the Yang-Mills flow associated to a holomorphic vector bundle E over an arbitrary compact K\"ahler manifold (X,{\omega}). In particular we show that the flow is determined at…

By the work of Hong and Tian it is known that given a holomorphic vector bundle E over a compact Kahler manifold X, the Yang-Mills flow converges away from an analytic singular set. If E is semi-stable, then the limiting metric is…

We study Brownian flows on manifolds for which the associated Markov process is strongly mixing with respect to an invariant probability measure and for which the distance process for each pair of trajectories is a diffusion $r$. We provide…

We provide abstract conditions which imply the existence of a robustly invariant neighbourhood of a global section of a fibre bundle flow. We then apply such a result to the bundle flow generated by an Anosov flow when the fibre is the…

Manifest T-duality covariance of the one-loop renormalization group flows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the…