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 …

In physics and in mathematics Z 2 n-gradings, n≥ 2, appear in various fields. The
corresponding sign rule is determined by the “scalar product” of the involved Z 2 n-degrees …

We propose a generalization of the classical Tulczyjew triple as a geometric tool in
Hamiltonian and Lagrangian formalisms which serves for contact manifolds. The role of the …

A new concept of Loday algebroid (and its pure algebraic version-Loday pseudoalgebra) is
proposed and discussed in comparison with other similar structures present in the literature …

In this paper, we consider some natural (functorial) lifts of geometric objects associated with
statistical manifolds (metric tensor, dual connections, skewness tensor, etc.) to higher …

A Lie system is a system of differential equations admitting a superposition rule, ie, a
function describing its general solution in terms of any generic set of particular solutions and …

We review origins and main properties of the most important bracket operations appearing
canonically in differential geometry and mathematical physics in the classical, as well as in …

Tulczyjew triple for physical systems with configuration manifold equipped with Lie group
structure is constructed and discussed. The case of systems invariant with respect to group …

In this paper we develop a geometric approach to higher order mechanics on graded
bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered …

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on
Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as …