In this article, we investigate Reeb dynamics on b m-contact manifolds, previously
introduced in [37], which are contact away from a hypersurface Z but satisfy certain …

A-dimensional Poisson manifold is said to be-symplectic if it is symplectic on the
complement of a hypersurface and has a simple Darboux canonical form at points of which …

In this paper, we analyze in detail a collection of motivating examples to consider bm-
symplectic forms and folded-type symplectic structures. In particular, we provide models in …

Motivated by the study of symplectic Lie algebroids, we focus on a type of algebroid (called
an E-tangent bundle) which is particularly well-suited to the study of singular differential …

This is the first in a series of papers dedicated to the study of Poisson manifolds of compact
types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via …

This monograph explores classification and perturbation problems for integrable systems on
a class of Poisson manifolds called $ b^ m $-Poisson manifolds. Even if the class of $ b^ m …

Within integrable systems, the class of so called" semitoric" integrable systems in dimension
four has attracted a lot of attention in recent years, especially since fundamental examples …

In this article, we introduce b-semitoric systems as a generalization of semitoric systems,
specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a …

The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds
is well-understood when the group under consideration is a torus (see, for …

Inspired by Arnold's classification of local Poisson structures [1] in the plane using the
hierarchy of singularities of smooth functions, we consider the problem of global …