Related papers: Bidimensional Symplectic Maps
We develop a general framework for studying phases of mixed states with strong and weak symmetries, including non-invertible or categorical symmetries. The central idea is to consider a purification of the mixed state density matrix, which…
We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…
We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess…
We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an…
Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates…
The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are…
A new family of strongly regular graphs, called the general symplectic graphs $Sp(2\nu, q)$, associated with nonsingular alternate matrices is introduced. Their parameters as strongly regular graphs, their chromatic numbers as well as their…
We introduce a practical approach to extract the symplectic transfer maps for arbitrary magnetic beam-line elements. Beam motion in particle accelerators depends on linear and nonlinear magnetic fields of the beam-line elements. These…
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterizations for volumetric parameterizations are known to fail…
We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis…
We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.
A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment…
Area-preserving nontwist maps locally violate the twist condition, giving rise to shearless curves. Nontwist systems appear in different physical contexts, such as plasma physics, climate physics, classical mechanics, etc. Generic…
This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality.…
In this paper, we study a particular conservative standard map in complex dimension 2. In this example, Siegel disks can be visualized and analyzed numerically as to the smoothness of their boundaries. We formulate and numerically support…