Related papers: On periodic homeomorphisms of spheres
The object of the present paper is to study the locally $\phi $- semisymmetric Kenmotsu manifolds along with the characterization of such notion.
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
There are (at least) two reasons to study random polytopes. The first is to understand the combinatorics and geometry of random polytopes especially as compared to other classes of polytopes, and the second is to analyze average-case…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for…
We survey the classification of the Riemannian metrics on spheres with respect to which all equators are minimal hypersurfaces, and discuss problems related to these geometries.
We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.
For a $C^{1}$ degree two latitude preserving endomorphism $f$ of the 2-sphere, we show that $f$ has $2^{n}$ periodic points.
This paper studies a class of $1\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of…
A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the…
Let S be a compact, oriented surface with negative Euler characteristic and let f be a homeomorphism of S that is isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector, then there exists a simple braid…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…
This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.
I review the origins and development of the idea of Dyson spheres, their purpose, their engineering, and their detectability. I explicate the ways in which the popular imagining of them as monolithic objects would make them dynamically…
We prove that either there exists at least one hamilton periodic orbit in a given energy close smooth hypersurface or there exist at least two hamilton periodic orbits in a near-by energy close smooth hypersurface. More general results also…
Relationship between quantum shell structure and classical periodic orbits is briefly reviewed on the basis of semi-classical trace formula. Using the spheroidal cavity model, it is shown that three-dimensional periodic orbits, which are…
The eigenfamilies of Gudmundsson and Sakovich can be used to generate harmonic morphisms, proper $r$-harmonic maps, and minimal co-dimension $2$ submanifolds. This article begins by characterising the globally defined eigenfamilies of the…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…