Related papers: Integrable mappings for noncommuting objects

Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of Arnold-Liouville and noncommutative integrability of Hamiltonian systems on symplectic manifolds to that on cosymplectic manifolds. We prove a variant of the…

We prove that 1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, 2) systems for commuting flows are Darboux integrable if and only if the…

The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…

A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The…

Two-dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n*3 dimensions. Even driven-dissipative deterministic dynamical systems…

We give a construction of completely integrable ($2n$)-dimensional Hamiltonian systems with symplectic brackets of the Lie-Poisson type (linear in coordinates) and with quadratic Hamilton functions. Applying to any such system the so called…

We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples we consider quantum mappings associated…

We study a complex intertwining relation of second order for Schroedinger operators and construct third order symmetry operators for them. A modification of this approach leads to a higher order shape invariance. We analyze with particular…

For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to…

The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may…

We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additional {\em quadratic} first integrals, thus constructing a large…

We give a construction of completely integrable 4-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with two Hermitian Hamilitonians the latter form…

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…

Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…

For a dynamical system we will construct various invariant sets starting from its conserved quantities. We will give conditions under which certain solutions of a nonlinear system are also solutions for a simpler dynamical system, for…