Related papers: Tangent ray foliations and their associated outer …
An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary, and also a circular scatterer in the interior of the disk. We investigate stability properties of some…
In the outer heliosphere, beyond the solar wind termination shock, it is expected that the warped heliospheric current sheet forms a region of closely-packed, multiple, thin current sheets. Such a system may be subject to the ion-kinetic…
The double-trace from UV to IR flow subtraction of infinities used earlier for the UV-convergent calculations of the Witten tadpole diagrams being applied to the bubble self-energy diagrams gives for them the amazingly simple expressions in…
Let $X$ be a smooth projective horospherical variety of Picard number one. We show that a uniruled projective manifold of Picard number one is biholomorphic to $X$ if its variety of minimal rational tangents at a general point is…
While billiard systems of various shapes have been used as paradigmatic model systems in the fields of nonlinear dynamics and quantum chaos, few studies have investigated anisotropic billiards. Motivated by the tremendous advances in using…
Polygonal billiards constitute a special class of models. Though they have zero Lyapunov exponent their classical and quantum properties are involved due to scattering on singular vertices. It is demonstrated that in the semiclassical limit…
We study codimension-two spacelike submanifolds in Lorentzian spacetimes that admit umbilical lightlike normal directions. We show that such submanifolds are subject to strong geometric and topological constraints, establishing explicit…
The aim of the paper is to unify the efforts in the study of integrable billiards within quadrics in flat and curved spaces and to explore further the interplay of symplectic and contact integrability. As a starting point in this direction,…
We prove that any vector field on a three-dimensional compact manifold can be approximated in the C1-topology by one which is singular hyperbolic or by one which exhibits a homoclinic tangency associated to a regular hyperbolic periodic…
Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…
The authors study the geometry of lightlike hypersurfaces on a four-dimensional manifold $(M, c)$ endowed with a pseudoconformal structure $c = CO (2, 2)$. They prove that a lightlike hypersurface $V \subset (M, c)$ bears a foliation formed…
This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain $D\subset \mathcal R^3$. Two models will be analysed: in the first one, only an inner Keplerian…
We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized…
In this paper, we study holomorphic foliations of degree four on complex projective space $\mathbb{P}^n$, where $n\geq 3$, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation…
There are multiple mappings that can be used to generate what we call the 'edge geometry' of a regular N-gon, but they are all based on piecewise isometries acting on the extended edges of N to form a 'singularity' set W. This singularity…
In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles and that satisfy a Weingarten condition of type $a H+b K=c$, where $a,b$ and $c$ are constant and $H$ and $K$ denote the mean curvature and the Gauss…
In our paper we study periodic geodesic motion on multidimensional ellipsoids with elastic impacts along confocal quadrics. We show that the method of isoperiodic deformation is applicable.
A qualitative analysis is given to the data on the full magnetic and velocity vector fields in a growing sunspot group, recorded nearly simultaneously with the Solar Optical Telescope on the Hinode satellite. Observations of a young bipolar…
We compute the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebra $\mathfrak{osp}_{2m-1|2n}(\mathbb C)$.
By using the public UV imaging data obtained by the GALEX (Galaxy Ultraviolet Explorer) for nearby galaxies, we have compiled a list of lenticular galaxies possessing ultraviolet rings - starforming regions tightly confined to particular…