Related papers: Star flows with singularities of different indices
Theories in 5 dimensions with minimal supersymmetry are studied for domain-wall solutions and in the context of the AdS/CFT correspondence. The scalar manifold is a product of a very special real manifold and a quaternionic-Kaehler…
Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle $\mathrm{PSL}_2(\mathbb{Z})\backslash\mathrm{PSL}_2(\mathbb{R})$. The complement of any finite number of orbits is a…
Phase transitions are uncommon among homogenous one-dimensional fluids of classical particles owing to a general non-existence result due to van Hove. A way to circumvent van Hove's theorem is to consider an interparticle potential that is…
Singularities of the Poynting vector field at resonant light scattering by nanoparticles are discussed and classified. It is shown that there are two generic types of them, namely (i) the singularities related to the vanishing of the…
The branched virtual fibering theorem by Sakuma states that every closed orientable $3$-manifold with a Heegaard surface of genus $g$ has a branched double cover which is a genus $g$ surface bundle over the circle. It is proved by Brooks…
A large class of stellar systems (e.g., planetary nebulae (PNe), supernova envelopes, LBV stars, young stars in formation) shows structures in their accretion/ejection phase that have similar characteristics. In particular, one currently…
The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound. This conjecture is known to be false in general due to a…
We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of $\mathrm{GL}(2,\mathbb{C})$ cocycles and establish a Johnson-type theorem for extended CMV matrices, relating the spectrum to the…
This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that \pi_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at…
We describe the equivalence classes of germs of generic $2$-parameter families of complex vector fields $\dot z = \omega_\epsilon(z)$ on $\mathbb{C}$ unfolding a singular parabolic point of multiplicity $k+1$: $\omega_0= z^{k+1}…
A stable map of a closed orientable $3$-manifold into the real plane is called a stable map of a link in the manifold if the link is contained in the set of definite fold points. We give a complete characterization of the hyperbolic links…
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…
The phenomenon of spectral mimicry refers to the fact that hypergiants and post-AGB supergiants - stars of different masses in fundamentally different stages of their evolution have similar optical spectra, and also share certain other…
A real matrix is Hurwitz if its eigenvalues have negative real parts. The following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS) is provided: Let $X:R^2-->R^2$ be a C^1 vector field whose derivative DX(p)…
In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on $\mathbb{P}^1$ and rank 2 (parabolic) Higgs bundle on $\mathbb{P}^1$. Then we obtain explicit descriptions of Zariski open…
Magnetic chemically peculiar (mCP) stars are strongly magnetic upper main-sequence stars that exhibit light rotational variability due to an uneven surface distribution of certain peculiar elements, which may appear in phase at certain…
Let $\psi$ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface $M$ for which $\psi$, when evaluated on $M$, coincides with the $m-$th elementary symmetric function of…
In [1] (hep-th/0211069), the author has discussed the quantum parameter space of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In…
In this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key…
It is conjectured that the recursive teaching dimension of any finite concept class is upper-bounded by the VC-dimension of this class times a universal constant. In this paper, we confirm this conjecture for two rich families of concept…