Related papers: Periodic eigendecomposition and its application to…
Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g. a trajectory ``p'' returns to its initial conditions after some fixed time tau_p. Our aim is to investigate the spectrum tau_1,…
The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…
We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…
Many-mode Floquet theory [T.-S. Ho, S.-I. Chu, and J. V. Tietz, Chem. Phys. Lett., v. 96, 464 (1983)] is a technique for solving the time-dependent Schr\"odinger equation in the special case of multiple periodic fields, but its limitations…
We investigate the singular value decomposition of a rectangular matrix that is analytic on the complex unit circumference, which occurs, e.g., with the matrix of transfer functions representing a broadband multiple-input multiple-output…
This thesis applies Floquet theory to analyze linear periodic time-varying (LPTV) systems, represented by a system of ordinary differential equations (ODEs) that depend on a time variable t and have a matrix of coefficients with period T>0.…
We present a new method for generating robust guesses for unstable periodic orbits (UPOs) by post-processing turbulent data using dynamic mode decomposition (DMD). The approach relies on the identification of near-neutral, repeated…
In this work, we show that the periodic defocusing Ablowitz-Ladik equation can be expressed as an isospectral deformation of Floquet CMV matrices. We then introduce a Poisson Lie group whose underlying group is a loop group and show that…
We review and further develop the recently introduced numerical approach for scattering calculations based on a so called pseudo-time Schroedinger equation, which is in turn a modification of the damped Chebyshev polynomial expansion…
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…
We report the first experimental observation of multiple transitions showing the emergence and disappearance of slowly decaying eigenmodes in a dissipative, Floquet electronic system with synthetic components. Conventional wisdom has it…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
In recent years we provided numerical methods based on pseudospectral collocation for computing the Floquet multipliers of different types of delay equations, with the goal of studying the stability of their periodic solutions. The latest…
In this survey article, we investigate the spectral properties of fractal differential operators on self-similar fractals. In particular, we discuss the decimation method, which introduces a renormalization map whose dynamics describes the…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
We study Floquet eigenspectra of a nonlinear two-mode system under a periodic driving of the off-diagonal coupling. By solving the Gross-Pitaevskii equation numerically, we obtain triangular and loop structures near the crossings of…
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in such a way that the orbits become stable. The main…
The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional…
In this paper, a new rigorous numerical method to compute fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. Decomposing the fundamental matrix solutions $\Phi(t)$ by their…
Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a…