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

The Newton-Raphson basins of attraction, associated with the libration points(attractors), are revealed in the generalized Hill problem. The parametricvariation of the position and the linear stability of the equilibrium points isdetermined, when the value of the perturbation parameter $\epsilon$ varies. Themultivariate Newton-Raphson iterative scheme is used to determine theattracting domains on several types of two-dimensional planes. A systematic andthorough numerical investigation is performed in order to demonstrate theinfluence of the perturbation parameter on the geometry as well as of the basinentropy of the basins of convergence. The correlations between the basins ofattraction and the corresponding required number of iterations are alsoillustrated and discussed. Our numerical analysis strongly indicates that theevolution of the attracting regions in this dynamical system is an extremelycomplicated yet very interesting issue.

Basins of convergence of equilibrium points in the generalized Hill problem