English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $q_{1}$,...,$q_{n}$ be the position vectors of the point masses of thecurved $n$-body problem. Consider any positive elliptic-elliptic rotopulsatorsolution$q_{i}^{T}=(r\cos{(\theta+\alpha_{i})},r\sin{(\theta+\alpha_{i})},\rho\cos{(\phi+\beta_{i})},\rho\sin{(\phi+\beta_{i})})$,$i\in\{1,...,n\}$, where $\alpha_{1},...,\alpha_{n},\beta_{1},...,\beta_{n}\in[0,2\pi)$ are constants, $\phi$, $\theta$, $r$ and $\rho$ aretwice-differentiable, continuous, nonconstant functions, $r^{2}+\rho^{2}=1$,$r\geq 0$ and $\rho\geq 0$. We prove that the if the configuration of the pointmasses is of nonconstant size, the configuration of the vectors  $(r\cos{(\theta+\alpha_{i})},r\sin{(\theta+\alpha_{i})})^{T}$ is a regularpolygon, as is the configuration of the vectors$(\rho\cos{(\phi+\beta_{i})},\rho\sin{(\phi+\beta_{i})})^{T}$,$i\in\{1,...,n\}$.

Positive elliptic-elliptic rotopulsators on Clifford tori of nonconstant size project onto regular polygons