相关论文: Dynamical realizations of l-conformal Newton-Hooke…

Dynamical systems invariant under the action of the l-conformal Newton-Hooke algebras are constructed by the method of nonlinear realizations. The relevant first order Lagrangians together with the corresponding Hamiltonians are found. The…

The method of nonlinear realizations is applied to the l-conformal Galilei algebra to construct a dynamical system without higher derivative terms in the equations of motion. A configuration space of the model involves coordinates, which…

By applying Niederer--like transformation, we construct a representation of the N=2 l-conformal Newton-Hooke superalgebra for the case of a negative cosmological constant in terms of linear differential operators as well as its dynamical…

Two Lagrangian formulations for describing of the damped harmonic oscillator have been introduced by Bateman. For these models we construct higher derivative generalization which enjoys the l-conformal Newton-Hooke symmetry. The dynamics of…

Dynamical systems which are invariant under N=1 supersymmetric extension of the l-conformal Galilei algebra are constructed. These include a free N=1 superparticle which is governed by higher derivative equations of motion and an N=1…

Based on the results in [Nucl. Phys. B 866 (2013) 212], we consider a way to construct a higher-derivative mechanical model which possesses the $l$-conformal Galilei symmetry. The dynamical system describes generalized Pais-Uhlenbeck…

We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of…

We consider the dynamics invariant under the action of l-conformal Galilei group using the method of nonlinear realizations. We find that by an appropriate choice of the coset space parametrization one can achieve the complete decoupling of…

In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013) 405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015) 031701], representation theory of the centrally extended l-conformal Galilei algebra with…

Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the…

We investigate an interacting Pais-Uhlenbeck oscillator with a Landau-Ginzburg type interaction term and analyse its classical dynamics from a geometric and numerical point of view. We show that the resulting fourth-order equation of motion…

The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this…

It is demonstrated that the Pais-Uhlenbeck oscillator in arbitrary dimension enjoys the l-conformal Newton-Hooke symmetry provided frequencies of oscillation form the arithmetic sequence omega_k=(2k-1) omega_1, where k=1,...,n, and l is the…

The method of nonlinear realizations is applied to construct new dynamical realizations of the Lifshitz group in mechanics, hydrodynamics, and field theory.

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…

We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…

We show explicitly how the Newton-Hooke groups act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes and show how…

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…

Motivated by the symmetry in the non-relativistic limit of anti-de Sitter geometry, we employ planar dynamical models featuring exotic (deformed) harmonic oscillators, presented through direct and indirect Lagrangian representations. The…