Related papers: Star fows and multisingular hyperbolicity

We consider the billiard flow of elastically colliding hard balls on the flat $\nu$-torus ($\nu\ge 2$), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the…

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if…

We present a hypersurface singularity in positive characteristic which is defined by a purely inseparable power series, and a sequence of point blowups so that, after applying the blowups to the singularity, the same type of singularity…

Let $\mathcal{F} $ be a pointwise almost periodic decomposition of a compact metrizable space $X$. Then $\mathcal{F} $ is $R$-closed if and only if $\hat{\mathcal{F}} $ is usc. Moreover, if there is a finite index normal subgroup $H$ of an…

We introduce two notions of hyperbolicity for not necessarily K\"ahler $n$-dimensional compact complex manifolds $X$. The first, called {\it balanced hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of Gauduchon's…

We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for $C^1$ flows, every sectional hyperbolic set $\Lambda$ is entropy expansive, and the topological entropy varies continuously with the…

The Galaxy's stellar halo seems to be a tangle of disrupted systems that have been tidally stretched out into streams. Each stream approximately delineates an orbit in the Galactic force-field. In the first paper in this series we showed…

The study of the kinematics of galaxies within clusters or groups has the limitation that only one of the three velocity components and only two of the three spatial components of a galaxy position in six-dimensional phase space can…

We argue that bulk spiral flows are ubiquitous in the cool cores (CCs) of clusters and groups of galaxies. Such flows are gauged by spiral features in the thermal and chemical properties of the intracluster medium, by the multi-phase…

We analyse the 2-dimensional distribution and kinematics of the stars as well as molecular and ionised gas in the central few hundred parsecs of 5 active and 5 matched inactive galaxies. The equivalent widths of the Br-gamma line indicate…

We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix…

If X is any connected Cayley graph on any finite abelian group, we determine precisely which flows on X can be written as a sum of hamiltonian cycles. (This answers a question of Brian Alspach.) In particular, if the degree of X is at least…

The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems with repulsive potentials by taking limit for a sequence of periodic solutions which are the minimizers of variational functional

Massive stars are extremely luminous and drive strong winds, blowing a large part of their matter into the galactic environment before they finally explode as a supernova. Quantitative knowledge of massive star feedback is required to…

Star complexes are the largest globular regions of star formation in galaxies. If there is a spiral density wave, nuclear ring, tidal arm, or other well-defined stellar structure, then gravitational instabilities in the gaseous component…

In this contribution I summarize our current knowledge of the nature and significance of starburst-driven galactic winds (``superwinds''). Superwinds are complex multiphase outflows of cool, warm, and hot gas, dust, and magnetized…

We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances…

A {\em singular hyperbolic attractor} for flows is a partially hyperbolic attractor with singularities (hyperbolic ones) and volume expanding central direction \cite{mpp1}. The geometric Lorenz attractor \cite{gw} is an example of a…

On a complete manifold, such as Euclidean 3-space or hyperbolic 3-space, the limit at infinity of the norm of the Higgs field is called the mass of the monopole. We show the existence, on hypebolic 3-space, of monopoles with given magnetic…