相关论文: The Dynamics of Off-center Reflection

This paper studies the behavior under iteration of the maps T_{ab}(x,y)=(F_{ab}(x)-y,x) of the plane R^2, in which F_{ab}(x)=ax if x>=0 and bx if x<0. The orbits under iteration correspond to solutions of the nonlinear difference equation…

This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.

We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…

We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…

We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.

The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…

We have adapted classical molecular dynamics to study the structural and dynamical properties of amorphous silica surfaces. Concerning the structure, the density profile exhibits oscillations perpendicularly to the surface as observed in…

A theoretical approach for the interpretation of reflectance spectra of opal photonic crystals with fcc structure and (111) surface orientation is presented. It is based on the calculation of photonic bands and density of states…

In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates):…

Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…

An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…

We present statistics on the decompositions (with respect to a distinguished symmetric 2t-cycle) of vertices of the hypercube graph, whose negative parts are covered by two subsets of the ground set {1,...,t} of the corresponding oriented…

Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…

The space ${\Bbb{L}}$ of oriented lines, or rays, in ${\Bbb{R}}^3$ is a 4-dimensional space with an abundance of natural geometric structure. In particular, it boasts a neutral K\"ahler metric which is closely related to the Euclidean…

We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…

This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.

Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…

In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized…