We make a local semi-analytical study of a quasi-periodic perturbation of the Sun-Jupiter RTBP Hamiltonian in a neighbourhood of the triangular points. First, we construct a suitable normal form of the Hamiltonian around the invariant torus that replaces L5. Then, we use this (high order) normal form to give a description of the local non-linear dynamics.

We calculate exactly the two bound Floquet modes of a periodic linear waveguide induced in a medium by a second-order soliton of the nonlinear Schrödinger equation. The modes are degenerate at the writing frequency, having the same quasi-propagation constant, which suggests applications of our method to spectral filtering.

Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasi-periodic Green's functions. The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method in Wu and Lu [J. Opt. Soc. Am. A 26, 2444 (2009)], [J. Opt. Soc. Am. A 28, 1191 (2011)] is a recently developed integral equation method that avoids the quasi-periodic Green's functio...

Quasi-periodic route to chaos is a common feature in DC-DC switching converters like the Boost and the Buck-Boost. A periodic orbit bifurcates into a T torus through a Neimark-Sacker bifurcation, and then, quasi-periodic behavior is obtained. Further changes in the parameters may breakdown such torus resulting in chaotic behavior. Analytical expressions are deduced for the stability character o...

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be represented by rational generating functions; a geometric characterization of such sets is also given. In addition, if p = (p1, . . . , pn) are a subset of the free...

In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover...

In this paper, an efficient short-time Fourier analysis method for the quasi-periodic signals is proposed via an optimal fixed-lag finite impulse response (FIR) smoother approach using a receding horizon scheme. In order to deal with time-varying Fourier coefficients (FCs) of quasi-periodic signals, a state space model including FCs as state variables is augmented with the variants of FCs. Thro...

Boundary integral equations are an important class of methods for acoustic and electromagnetic scattering from periodic arrays of obstacles. For piecewise homogeneous materials, they discretize the interface alone and can achieve high order accuracy in complicated geometries. They also satisfy the radiation condition for the scattered field, avoiding the need for artificial boundary conditions ...

In this paper we find an upper bound for the maximum number of limit cycles bifurcating from the periodic orbits of any planar polynomial quasi-homogeneous center, which can be obtained using first order averaging method. This result improves the upper bounds given in [7].

The paper considers non-autonomous oscillatory systems of ordinary differential equations with d ≥ 1 nonresonant constant frequencies. Formal series like those used nowadays to analyze the properties of numerical integrators are employed to construct higher-order averaged systems and the required changes of variables. With the new approach, the averaged system and the change of variables consis...