We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around...

Studying of mutual coupling parameters between the antenna elements in an array environment has been considered as the subject of feature research. That is why, in this paper, we present a new Floquet modal analysis procedure for analyzing almost periodic structures. Accurate evaluation of the mutual coupling could be achieved by this analysis. It is shown how Floquet analysis can be exploited ...

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the pe...

In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental matrix solution Φ(t) is a canonical decomposition of the form Φ(t) = Q(t)e, where Q(t) is a real periodic matrix and R is a constant matrix. To compute rigorously the Fl...

We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the (t, t) Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables within the theory. We show that the geometric phases are then identified with horizontal lifts of surfaces in an abelian gerbe with connection, rather than with ...

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct homotopy classes and give a simple phys...

We study the quantum version of a tilting and flashing Hamiltonian ratchet, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the corresponding Hamiltonian. The dc-current appears due to the desymmetrization of Floquet eigenstates, which become transporting when all the relevant symmetries ...

We present an algorithm for the computation of reducible quasi-periodic solutions of discrete dynamical systems. The method is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear sta...

Photodissociations induced by intense short laser pulses are investigated using a generalized Floquet formulation. This formulation replaces the continuous electric eld shape function by a discrete step function. An initial active space is deened by using the Bloch's wave operator theory and the corresponding target spaces, in which the dynamics is connned, are built for each new discrete value...