Related papers: Analytic integrability of two lopsided systems
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…
We introduce two-sided type systems, which are sequent calculi for typing formulas. Two-sided type systems allow for hypothetical reasoning over the typing of compound program expressions, and the refutation of typing formulas. By…
We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…
The main purpose of this article is to study from the geometric point of view the problem of limit cycles bifurcation of perturbed completely integrable systems.
We present an analytical and numerical investigation of double-slit diffraction under coherent illumination by three plane waves: one normally incident and two symmetrically angled at plus/minus theta. By imposing an edge-zero condition on…
The orbits of the reversible differential system $\dot{x}=-y$, $\dot{y}=x$, $\dot{z}=0$, with $x,y \in R$ and $z\in R^d$, are periodic with the exception of the equilibrium points $(0,0, z)$. We compute the maximum number of limit cycles…
The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type corrections for large volumes of the vacuum energy for integrable theories with…
We focus on the second part of Hilbert's 16th problem and provide an upper bound on the number of limit cycles that a polynomial, differential, planar system may have, depending exclusively on the degree $n$ of the system. Such a bound…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form.…
In this paper, we give sufficient conditions under which linear abstract control systems for which the semigroup is analytic are stabilizable with a bounded feedback. We obtain various characterizations of that property, which extend some…
In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the $SU(2)_{k}\otimes SU(2)_{l}/SU(2)_{k+l}$ coset conformal field theories…
We study the set of intrinsic singularities of flat affine systems with $n-1$ controls and $n$ states using the notion of Lie-B\"acklund atlas, previously introduced by the authors. For this purpose, we prove two easily computable…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable mappings, a subclass of symplectic mappings, are equivalent to…
The path integral of Liouville theory is well understood only when the central charge $c\in [25, \infty)$. Here, we study the analytical continuation the lattice Liouville path integral to generic values of $c$, with a particular focus on…