We will present a consistent description of Hamiltonian dynamics on the'symplectic
extended phase space'that is analogous to that of a time-independent Hamiltonian system …

In the paraxial regime of Newtonian optics, propagation of an ensemble of rays is
represented by a symplectic ABCD transfer matrix defined on a reduced phase space. Here …

An exact invariant is derived for n‐degree‐of‐freedom non‐relativistic Hamiltonian systems
with general time‐dependent potentials. To work out the invariant, an infinitesimalcanonical …

An effective operational approach to quantum mechanics is to focus on the evolution of
wave packets, for which the wave function can be seen in the semi-classical regime as …

The notion of integrability is discussed for classical nonautonomous systems with one
degree of freedom. The analysis is focused on models which are linearly spanned by finite …

Following the main principles of developing the evolutionary nonlinear integrable systems
on quasi-one-dimensional lattices, we suggest a novel nonlinear integrable system of …

The Struckmeier and Riedel (SR) approach is extended in real space to isolate dynamical
invariants for one-and two-dimensional time-dependent Hamiltonian systems. We further …

This paper explores a mathematical technique for deriving dynamical invariants (ie
constants of motion) in time-dependent gravitational potentials. The method relies on the …

Noether and Lie symmetry analyses based on point transformations that depend on time
and spatial coordinates will be reviewed for a general class of time-dependent Hamiltonian …

Exact quadratic in momenta complex invariants are investigated for both time independent
and time dependent one-dimensional Hamiltonian systems possessing higher order …