Related papers: Vector Field Induced Chaos in Multi-dimensional Ho…

We study here the unhindered gravitational collapse of spatially homogeneous (SH) scalar fields $\phi$ with a potential $V_{s}(\phi)$, as well as vector fields $\tilde{A}$ with a potential $V_{v}(B)$ where $B=g(\tilde{A},\tilde{A})$ and $g$…

Let $\mathscr{X}^r(M)$ be the set of $C^r$ vector fields on a boundaryless compact Riemannian manifold $M$. Given a vector field $X_0\in\mathscr{X}^r(M)$ and a compact invariant set $\Gamma$ of $X_0$, we consider the closed subset…

Starting from some remarkable singularities of holomorphic vector fields, we construct (open) complex surfaces over which the singularities in question are realized by complete vector fields. Our constructions lead to manifolds and vector…

This is a complete study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a contracting homogeneous polynomial. The contracting nonlinearity provides the…

Horndeski derived a most general vector-tensor theory in which the vector field respects the gauge symmetry and the resulting dynamical equations are of second order. The action contains only one free parameter, $\lambda$, that determines…

We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous…

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…

We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically…

In this paper, we characterize arbitrary polynomial vector fields on $S^n$. We establish a necessary and sufficient condition for a degree one vector field on the odd-dimensional sphere $S^{2n-1}$ to be Hamiltonian. Additionally, we…

We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the universe and carry out a…

We consider the cosmological implications of a gravitational theory containing two vector fields coupled minimally to gravity as well as a generalized Chern-Simons term that couples the two vector fields. One of the vector fields is the…

This paper is about the integrability of complex vector fields in dimension three in a neighborhood of a singular point. More precisely, we study the existence of holomorphic first integrals for isolated singularities of holomorphic vector…

A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test…

We consider several new classes of viable vector field alternatives to the inflaton and quintessence scalar fields. Spatial vector fields are shown to be compatible with the cosmological anisotropy bounds if only slightly displaced from the…

Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations,…

A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard…

A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz…

Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a…

We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the…