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

We consider the $n$--body problem defined on surfaces of constant negativecurvature. For the case of $n$--equal masses we prove that the hyperbolicrelative equilibria with a regular polygonal shape do not exist. In particularthe Lagrangian (three equal distances) hyperbolic relative equilibria do notexist. We also show the existence of a new class of hyperbolic collinearrelative equilibria for the five body problem on surfaces of constant negativecurvature.

On the non-existence of hyperbolic polygonal relative equilibria for the negative curved $n$--body problem with equal masses