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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The configuration space of the planar three-body problem when collisions areexcluded has a rich topology which supports a large set of free homotopyclasses. Most classes survive modding out by rotations. Those that survive arecalled the reduced free homotopy classes and have a simple description whenprojected onto the shape sphere. They are coded by syzygy sequences. We provethat every reduced free homotopy class, and thus every reduced syzygy sequence,is realized by a reduced periodic solution to the Newtonian planar three-bodyproblem. The realizing solutions have nonzero angular momentum, repeatedly comevery close to triple collision, and have lots of "stutters"--repeated syzygiesof the same type. The heart of the proof is contained in the work by one of uson symbolic dynamics arising out of the central configurations after the triplecollision is blown up using McGehee's method.

Realizing All Free Homotopy Classes for the Newtonian Three-Body Problem