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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We present a collection of examples borrowed from celestial mechanics andprojective dynamics. In these examples symplectic structures with singularitiesarise naturally from regularization transformations, Appell's transformation orclassical changes like McGehee coordinates, which end up blowing up thesymplectic structure or lowering its rank at certain points. The resultinggeometrical structures that model these examples are no longer symplectic butsymplectic with singularities which are mainly of two types: $b^m$-symplecticand $m$-folded symplectic structures. These examples comprise the three bodyproblem as non-integrable exponent and some integrable reincarnations such asthe two fixed-center problem. Given that the geometrical and dynamicalproperties of $b^m$-symplectic manifolds and folded symplectic manifolds arewell-understood [GMP, GMP2, GMPS, KMS, Ma, CGP, GL,GLPR, MO, S, GMW], weenvisage that this new point of view in this collection of examples can shedsome light on classical long-standing problems concerning the study ofdynamical properties of these systems seen from the Poisson viewpoint.

Examples of integrable and non-integrable systems on singular symplectic manifolds