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

Three types of orbits are theoretically possible in autonomous Hamiltoniansystems with three degrees of freedom: fully chaotic (they only obey the energyintegral), partially chaotic (they obey an additional isolating integralbesides energy) and regular (they obey two isolating integrals besides energy).The existence of partially chaotic orbits has been denied by several authors,however, arguing either that there is a sudden transition from regularity tofull chaoticity, or that a long enough follow up of a supposedly partiallychaotic orbit would reveal a fully chaotic nature. This situation needsclarification, because partially chaotic orbits might play a significant rolein the process of chaotic diffusion. Here we use numerically computed Lyapunovexponents to explore the phase space of a perturbed three dimensional cubicforce toy model, and a generalization of the Poincar\'e maps to show thatpartially chaotic orbits are actually present in that model. They turn out tobe double orbits joined by a bifurcation zone, which is the most likely sourceof their chaos, and they are encapsulated in regions of phase space bounded byregular orbits similar to each one of the components of the double orbit.

Partially chaotic orbits in a perturbed cubic force model