Related papers: Ballistic Transport for Periodic Jacobi Operators …
We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic nonalgebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we…
Topological protection allows robust transport of localized phenomena such as quantum information, solitons, and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically…
This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas.…
In this paper, we show that billiard orbits in rational polygons and geodesics on translation surfaces exhibit super-fast spreading, an optimal time-quantitative majority property about the corresponding linear flow that implies uniformity…
We obtain a perturbative proof of localization for quasiperiodic operators on $\ell^2(\Z^d)$ with one-dimensional phase space and monotone sampling functions, in the regime of small hopping. The proof is based on an iterative scheme which…
We study transport properties of Schr\"odinger operators depending on one or more parameters. Examples include the kicked rotor and operators with quasi-periodic potentials. We show that the mean growth exponent of the kinetic energy in the…
We prove that the combinatorics generated by the quantum random walk on Z can be interpreted from the reading of periodic orbits of the classical chaotic map $x \mapsto 2x mod 1$.
We prove the existence of $n$-periodic orbits for almost all $n\in\mathbb{N}$ in the R\"ossler system with attracting periodic orbit, for two sets of parameters. The proofs are computer-assisted.
We prove that of the creator operators, on the $d$ commuting indeterminates polynomial algebra, are linearly independent. We further study the connection between the classical (one dimensional) and the multi-dimensional ($d$-dimensional, $d…
The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
In this paper we study spectral properties of Jacobi operators. In particular, we prove two main results: (1) that perturbing the diagonal coefficients of Jacobi operator, in an appropriate sense, results in exponential localization, and…
The aim of this work is to report on several ladder operators for generalized Zernike polynomials which are orthogonal polynomials on the unit disk $\mathbf{D}\,=\,\{(x,y)\in \mathbb{R}^2: \; x^2+y^2\leqslant 1\}$ with respect to the weight…
Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B, $$ with…
Motivated by the study of the asymptotic behavior of Jacobi polynomials $\left( P_{n}^{(nA,nB)}\right) _{n}$ with $A\in \mathbb C$ and $B>0$ we establish the global structure of trajectories of the related rational quadratic differential on…
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is…
Periodic lattices are natural generalizations of lattices, which arise naturally in diophantine approximations with rationals of bounded denominators. In this paper, we prove analogues of classical theorems in geometry of numbers for…
We study spaces of reflectionless Jacobi matrices. The main theme is the following type of question: Given a reflectionless Jacobi matrix, is it possible to approximate it by other reflectionless and, typically, simpler Jacobi matrices of a…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information on well-posedness, and stability of solutions. These notes…