A bstract We study the boundary description of the volume of maximal Cauchy slices using
the recently derived equivalence between bulk and boundary symplectic forms. The volume …

Plane gravitational waves can admit a sixth 'screw'isometry beyond the usual five. The same
is true of plane electromagnetic waves. From the point of view of integrable systems, a sixth …

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 …

Understanding complex systems with their reduced model is one of the central roles in
scientific activities. Although physics has greatly been developed with the physical insights …

We communicate through this work the fractional calculus of variations and its
corresponding Euler–Lagrange equations in 1D constrained holonomic, non-holonomic …

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 …

In this paper we present an approach toward the comprehensive analysis of the
nonintegrability of differential equations in the form ̈x=f(x,t) which is analogous to …

An exact invariant is derived for n-degree-of-freedom Hamiltonian systems with general time-
dependent potentials. The invariant is worked out in two equivalent ways. In the first …

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 …

We investigate the transformation of initial conditions for primordial curvature perturbations
under two types of transformations of the associated action: simultaneous redefinition of time …