Motivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a b-Lie group as a pair where G is a Lie group and H is a codimension-one Lie ...

We define the Bohr-Sommerfeld quantization via T -modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [Victor W. Guillemin, Eva Miranda, and Jonathan Weitsman. On ...

The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of k-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of ...

Given a normally hyperbolic invariant manifold $\Lambda$ for a map $f$, whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an ...

We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent ...

In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes ...

It is well-known that the Poisson reduction of a hamiltonian system on the cotangent bundle of a manifold produces a hamiltonian system on a linear Poisson manifold. On the other hand, linear Poisson structures on a vector ...

Morse homology studies the topology of smooth manifolds by examining the critical points of a real-valued function defined on the manifold, and connecting them with the negative gradient of the function. Rather surprisingly, ...

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of ...

Motivated by Poincare’s orbits going to infinity in the (restricted) three-body problem ´ (see [29] and [7]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a ...