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 extend the investigation of three-dimensional (3D) Hamiltonian systems ofnon-subgroup type admitting non-zero magnetic fields and an axial symmetry,namely the circular parabolic case, the oblate spheroidal case and the prolatespheroidal case. More precisely, we focus on linear and some special cases ofquadratic superintegrability. In the linear case, no new superintegrable systemarises. In the quadratic case, we found one new minimally superintegrablesystem that lies at the intersection of the circular parabolic and cylindricalcases and another one at the intersection of the cylindrical, spherical, oblatespheroidal and prolate spheroidal cases. By imposing additional conditions onthese systems, we found for each quadratically minimally superintegrable systema new infinite family of higher-order maximally superintegrable systems. Thesetwo systems are linked respectively with the caged and harmonic oscillatorswithout magnetic fields through a time-dependent canonical transformation.

On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields