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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study solutions of the Newtonian $n$-body problem which tend to infinityhyperbolically, that is, all mutual distances tend to infinity with nonzerospeed as $t \rightarrow +\infty$ or as $t \rightarrow -\infty$. In suitablecoordinates, such solutions form the stable or unstable manifolds of normallyhyperbolic equilibrium points in a boundary manifold "at infinity". We showthat the flow near these manifolds can be analytically linearized and use thisto give a new proof of Chazy's classical asymptotic formulas. We also addressthe scattering problem, namely, for solutions which are hyperbolic in bothforward and backward time, how are the limiting equilibrium points related?After proving some basic theorems about this scattering relation, we useperturbations of our manifold at infinity to study scattering "near infinity",that is, when the bodies stay far apart and interact only weakly.

Chazy-Type Asymptotics and Hyperbolic Scattering for the $n$-Body Problem