Ġ = {G,H}. In particular, the DV F is called an integral if it has zero PB with the Hamiltonian {F,H} = 0. In this case F does not depend on t. In many problems of the classical mechanics DV form elegant algebraic structures which are closed with respect to PB. The Poisson structures with non-linear PB were discussed in [9] and [6]. Sklyanin introduced [9] the so-called quadratic Poisson algebr...

We show how the formal theory of diierential equations provides a unifying framework for some aspects of constrained Hamiltonian systems and of the numerical analysis of diierential algebraic equations, respectively. This concerns especially the Dirac algorithm for the construction of all constraints and various index concepts for diierential algebraic equations. 1. Introduction Constrained Ham...

This work is concerned with the Hamiltonian field formulation of the equations that describe two-dimensional non-dissipative gyroviscous onefluid plasmas [I, 2, 3, 4J. These equations differ from the usual Eulerian form of ideal MHO by the inclusion of a non-entropy-producing stress tensor that arises from the finiteness of the ion gyroradius. The physics of this stress \ensor is important for ...

We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of b frequencies, b ≤ d + 2, in arbitrary dimension d and for arbitrary non integrable algebraic nonlinearity p. This reflects the conservation of d momenta, energy and L norm. In 1d, we prove the existence of quasi-periodic solutions with arbit...

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems are intractable solve on classical computer. Current generation noisy intermediate-scale (NISQ) computers severely limited in terms chip size and error rates. Shallow circuits with uncomplicated topologies essential successful applications NISQ er...

We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation control. The structure is ideal for automated network-based since it invariant under power-conserving interconnection, congruence transformations Galerkin projection. Moreover, stability passivity properties are easily shown. Condensed forms orthogonal present easy analysis tools exis...

Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie algebras beyond Jordan ones may be useful for a description of almost periodic, asymptotically periodic, almost asymptotically periodic, and possibly, more cha...

Implicit and explicit representations of smooth, finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations. Explicit representations are derived when ...