Related papers: Canonical methods of constructing invariant tori b…
Let X be a smooth complex projective variety of dimension n equipped with a very ample Hermitian line bundle L. In the first part of the paper, we show that if there exists a toric degeneration of X satisfying some natural hypotheses (which…
Consider a sufficiently smooth nearly integrable Hamiltonian system of two and a half degrees of freedom in action-angle coordinates \[ H_\epsilon (\varphi,I,t)=H_0(I)+\epsilon H_1(\varphi,I,t), \varphi\in T^2,\ I\in U\subset R^2,\ t\in…
A non-iterative method for the construction of the Short-Time Fourier Transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of…
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…
A method via the KAM technique is introduced to study the existence of invariant tori and quasiperiodic solutions for impulsive Duffing-type equations with time period 1. Basing on several planar symplectic homeomorphisms and some estimates…
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…
A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying…
Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete…
Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko…
The integral expression for gravitational potential of a homogeneous circular torus composed of infinitely thin rings is obtained. Approximate expressions for torus potential in the outer and inner regions are found. In the outer region a…
In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical…
We develop an iterative technique for computing the unstable and stable eigenfunctions of the invariant tori of diffeomorphisms. Using the approach of Jorba, the linearized equations are rewritten as a generalized eigenvalue problem.…
We prove that the recently developed semiexplicit symplectic integrators for non-separable Hamiltonian systems preserve any linear and quadratic invariants possessed by the Hamiltonian systems. This is in addition to being symmetric and…
Advances in engineering mesoscopic quantum devices have led to new material platforms where electronic transport can be achieved on foldable structures. In this respect, we study quantum phases and their transitions on a Kirigami structure,…
We revisit an algorithm constructing elliptic tori, that was originally designed for applications to planetary hamiltonian systems. The scheme is adapted to properly work with models of chains of $N+1$ particles interacting via anharmonic…
We investigate invariant canonical transformations of a spatially covariant scalar-tensor theory of gravity, called the XG theory, by which the action or the Hamiltonian and the primary constraints keep their forms invariant. We derive the…
New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial…