Related papers: An example of a vector field with the oriented sha…
In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…
Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous…
It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several…
We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static…
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
The $\pi$-exterior derivative ${\o}d$, which is the Finslerian generalization of the (usual) exterior derivative $d$ of Riemannian geometry, is defined. The notion of a ${\o}d$-closed vector field is introduced and investigated. Various…
Conformal fields are a recently discovered class of representations of the algebra of vector fields in $N$ dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed.
We show that that vector field-based models of the ether generically do not have a Hamiltonian that is bounded from below in a flat spacetime. We also demonstrate that these models possess multiple light cones in flat or curved spacetime,…
This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth…
We give a class of examples of vector bundles on a relative smooth projective curve over Spec Z such that for infinitely many prime reductions the bundle has a Frobenius descent, but the restriction to the generic fiber in characteristic…
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the…
Our object of study is non smooth vector fields on $\R^2$. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way we are able to bring out some results that…
Negative propagation is an uncommon response produced by the local sign change in Poynting vector components. We present a general Poynting vector expression for all invariant beams with cylindrical symmetry using scalar potentials in order…
We study the equivalence principle, regarded as the cornerstone of general relativity, by analyzing the deformation observable of black hole shadows. Such deformation can arise from new physics and may be expressed as a phenomenological…
We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.
We describe all possible topological structures of codimension one gradient vector fields on the shpere with at most ten singular points. To describe structures, we use a graph whose edges are one-dimensional stable manifolds. The…
An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…
We identify a general class of spacetime metrics that mimic the properties of black holes without possessing a true event horizon. These metrics are constrained by the requirements of being singularity-free and geodesically complete.…
We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…