Related papers: General unit-disk representation for periodic mult…
We study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momentum, we find some disk-like global surfaces of section with…
We study the reflectional symmetry of a surface in the Euclidean 3-dimensional space with a cross-cap singularity with respect to planes. This symmetry is picked up by the singularities of folding maps on the cross-cap. We give a list of…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of three different phase space geometries (planar, hyperbolic or…
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.
In the turbulent regime of coupled map lattice with non-local interaction the maps systematically form periodic cluster attractors and their remnants by synchronization due to the foliation of periodic windows of the element map. We examine…
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…
Spatial gaps correspond to the projection in position space of the gaps of a periodic structure whose envelope varies spatially. They can be easily generated in cold atomic physics using finite-size optical lattice, and provide a new kind…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
In this paper, we introduce the concept of central periodic points of a linear system as points which lies on orbits starting and ending at the central subgroup of the system. We show that this set is bounded if and only if the central…
Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…
We use quantum invariants to define an analytic family of representations for the mapping class group of a punctured surface. The representations depend on a complex number A with |A| <= 1 and act on an infinite-dimensional Hilbert space.…
In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
For chaotic classical systems, the distribution of return times to a small region of phase space is universal. We propose a simple tool to investigate multiple returns in quantum systems. Numerical evidence for the baker map and kicked top…
We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two sets of generalized reflection equations with associated consistent fusion procedures. Products of their…
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a…
We study a variant of intersection representations with unit balls, that is, unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far sets, the goal is to…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
For typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and that the product of the cocycle along its orbit is a proximal…