We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the
one dominating in the literature, serves also for non-trivial contact structures. In this …

We present an approach to Jacobi and contact geometry that makes many facts, presented
in the literature in an overcomplicated way, much more natural and clear. The key concepts …

We present a new method to analytically prove global stability in ghost-ridden dynamical
systems. Our proposal encompasses all prior results and consequentially extends them. In …

Graded bundles are a class of graded manifolds which represent a natural generalisation of
vector bundles and include the higher order tangent bundles as canonical examples. We …

We define and make initial study of Lie groupoids equipped with a compatible homogeneity
(or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One …

Motivated by properties of higher tangent lifts of geometric structures, we introduce concepts
of weighted structures for various geometric objects on a manifold F equipped with a …

The equations for the critical points of the action functional defined by a Lagrangian
depending on higher-order derivatives of admissible curves on a Lie algebroid are found …

We give a method to construct Poisson brackets {⋅,⋅} on Banach manifolds M, for which the
value of {f, g} at some point may depend on higher order derivatives of the smooth functions …

The aim of this work is to study, from an intrinsic and geometric point of view, second-order
constrained variational problems on Lie algebroids, that is, optimization problems defined by …

We construct the full linearisation functor which takes a graded bundle of degree $ k $(a
particular kind of graded manifold) and produces a $ k $-fold vector bundle. We fully …