相关论文: General unit-disk representation for periodic mult…

We exhibit a single interval map (called universal map) that admits all those orbit patterns which are available in the first Sharkovsky class. An interval map is said to be in the first Sharkovsky class if every periodic point of it is a…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is…

We construct a subset $A$ of the unit disc with the following properties. (i) The set $A$ is the finite union of disjoint line segments. (ii) The shadow of $A$ is arbitrarily close to the shadow of the unit disc in "most" directions. (iii)…

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed…

For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…

Interference phenomena are the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive…

Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the…

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…

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…

We develop a framework to describe a wide class of flat-band models, with and without a translational symmetry, by using "molecular orbitals" introduced in the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011)…

One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…

It is known that the universal cover of compact Riemann surface is either the projective line, the complex plane or the unit disk. In this article we construct a very explicit family of complex surfaces that gives rise to uncountably many…

The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…

The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and…

The P-matrix approach for the determination of the orbit spaces of compact linear groups enabled to determine all orbit spaces of compact coregular linear groups with up to 4 basic polynomial invariants and, more recently, all orbit spaces…

We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which the diffeomorphisms have arbitrarily large finite numbers of…