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 prove the existence of chaotic motions in a planar restricted four bodyproblem, establishing that the system is not integrable. The idea of the proofis to verify the hypotheses of a topological forcing theorem. The forcingtheorem applies to two freedom Hamiltonian systems where the stable andunstable manifolds of a saddle-focus equilibrium intersect transversally in theenergy level set of the equilibrium. We develop a mathematically rigorouscomputer assisted argument which verifies the hypotheses of the forcingtheorem, and we implement our approach for the restricted four body problem.The method is constructive and works far from any perturbative regime and fornon-equal masses. Being constructive, our argument results in useful byproductslike information about the locations of transverse connecting orbits,quantitative information about the invariant manifolds, and upper/lower boundson transport times.

Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem