Related papers: Star fows and multisingular hyperbolicity
Close-in exoplanets interact with their host stars gravitationally as well as via their magnetized plasma outflows. The rich dynamics that arises may result in distinct observable features. Our objective is to study and classify the…
Flows of vector fields are an essential tool in differential geometry, with countless applications in both theory and practice. While they have been extensively studied for ordinary manifolds and supermanifolds, a treatment of flows in…
Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in…
In this paper, we first consider a class of expanding flows of closed, smooth, star-shaped hypersurface in Euclidean space $\mathbb{R}^{n+1}$ with speed $u^\alpha f^{-\beta}$, where $u$ is the support function of the hypersurface, $f$ is a…
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of…
This article is a first step towards the understanding of the dynamics of the horocycle flow on foliated manifolds by hyperbolic surfaces. This is motivated by a question formulated by M. Martinez and A. Verjovsky on the minimality of this…
In this article we prove that if a flow exhibits a partially hyperbolic attractor and it has two periodic saddles with different indices, and the stable index of one of them coincides with the dimension of strongly stable bundles, then it…
Different hydrodynamic regimes for the gaseous outflows generated by multiple supernovae explosions and stellar winds occurring within compact and massive star clusters are discussed. It is shown that there exists the threshold energy that…
Various galaxy properties are not continuous over a large range in mass, but rather reveal a remarkable transition or `bimodality' at a stellar mass of 3 x 10^{10} Mo. These properties include colors, stellar populations, Xray emission and…
A typical galaxy consists of a huge number of stars attracted to each other by gravity. For instance, the Milky Way has about $10^{11}$ stars. Thus it is typically modeled by the Vlasov-Poisson system. We prove an existence theorem for…
Hypersonic bipolar outflows are a ubiquitous phenomena associated with both young and highly evolved stars. Observations of Planetary Nebulae, the nebulae surrounding Luminous Blue Variables such as $\eta$ Carinae, Wolf Rayet bubbles, the…
In this paper we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual…
We show that hydrodynamic turbulent cloud simulations naturally produce large filaments made up of a network of smaller and coherent sub-filaments. Such simulations resemble observations of filaments and fibres in nearby molecular clouds.…
The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms. One meets difficulties when one tries to extend these definitions to vector fields and Shantao…
We have computed the galactic trajectories of twelve hypervelocity stars (HVSs) under the assumption that they originated in the Galactic Centre. We show that eight of these twelve stars are bound to the Galaxy. We consider the subsequent…
We present a simple phenomenological model of star formation in galaxies that describes the process with a set of a few parameters. The star formation efficiency and the fraction of gas and metals ejected in outflows are assumed to be the…
For any $n$-dimensional smooth manifold $\Sigma$, we show that all the singularities of the mean curvature flow with any initial mean convex hypersurface in $\Sigma$ are cylindrical (of convex type) if the flow converges to a smooth…
The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of periodic solutions which are the variational minimizers of Lagrangian actions.
As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometer or so is expected to freeze to form an elastic crust of increasingly neutron-rich…
Let $G$ be an acylindrically hyperbolic group. We prove that Bernoulli bond percolation on every Cayley graph of $G$ has a nonuniqueness phase, in which there are infinitely many infinite clusters. This generalizes Hutchcroft's result for…