相关论文: The Dynamics of Off-center Reflection

Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic…

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich…

Motivated by the rich theory of harmonic maps from a 2-sphere, we study biharmonic maps from a 2-sphere in this paper. We first derive biharmonic equation for rotationally symmetric maps between rotationally symmetric 2-manifolds. We then…

We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…

There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary…

We study dynamical systems that switch between two different vector fields depending on a discrete variable and with a delay. When the delay reaches a problem-dependent critical value so-called event collisions occur. This paper classifies…

A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map an elliptic curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich…

Any affine map on the (n+1)-dimensional Euclidean space gives rise to a natural map on the n-dimensional sphere whose dynamical aspects are not so well-studied in the literature. We explore the dynamical aspects of these maps by…

We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…

Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…

Geometrically decorated two-dimensional (2D) discrete surfaces can be more effective than conventional smooth reflectors in managing wave radiation. Constructive non-specular wave scattering permits the scattering angle to be other than…

In this paper we will study families of circle maps of the form $x\mapsto x+2\pi r + a f(x) \pmod{2\pi}$ and investigate how many periodic trajectories maps from this family can have for a "typical" function $f$ provided the parameter $a$…

Light beams can be symmetric under different transformations: translations, rotations, mirror symmetries, duality transformations, etc. In this thesis, a systematic way of characterizing these symmetries is presented. Then, it is shown that…

A spherical periscope in multi-dimensional space is a system of two ideal mirrors that reflect the rays emanating from a fixed point to the rays coming back to the same point, and a reversed periscope is a system of two mirrors that reflect…

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…

Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…

The frequency shift of a helical light beam experiencing the rotation near the axis deferring from its own axis (conical evolution) is studied theoretically. Both the energy and the kinematic approaches lead to a paradoxical conclusion that…