Related papers: Higher order first integrals of autonomous dynamic…

In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…

Liouville integrable separable systems with quadratic in momenta first integrals are considered. Particular attention is paid to the systems generated by the so-called special conformal Killing tensors, i.e. Benenti systems. Then,…

A first-principles method, based on density functional perturbation theory, is presented for computing the leading order tunability of high-dielectric-constant materials.

Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce…

The spectral method for building first integrals of ordinary linear differential systems is elaborated. Using this method, we obtain bases of first integrals for linear differential systems with constant coefficients, for linear…

In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…

We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…

The question of how Algebra can be used to solve dynamical systems and characterize chaos was first posed in a fertile mathematical context by Ziglin, Morales, Ramis and Sim\'o using differential Galois theory. Their study was aimed at…

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…

This paper develops a structure-preserving numerical integration scheme for a class of higher-order mechanical systems. The dynamics of these systems are governed by invariant variational principles defined on higher-order tangent bundles…

For a class of Hamiltonian systems naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional integrals of motion.

The higher-order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals) a third integral of higher-order in the momenta that can be obtained as the…

We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…

Recently one integrable model with a cubic first integral of motion has been studied by Valent using some special coordinate system. We describe the bi-Hamiltonian structures and variables of separation for this system.

The integrable time-dependent central potentials that admit linear and quadratic first integrals other than those constructed from the angular momentum are determined. It is shown explicitly that previous answers to this problem are…

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…

The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm…