Related papers: McMillan map and nonlinear Twiss parameters
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…
We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
We consider a class of matrices with a specific structure that arises, among other examples, in dynamic models for biological regulation of enzyme synthesis (Tyson and Othmer, 1978). We first show that a stability condition given in (Tyson…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the parameter of the map and the fractional order of the…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some approachable one-parameter families of rational maps; the goal…
We develop a general framework to describe the cubically nonlinear interaction of a unidirectional degenerate quartet of deep-water gravity waves. Starting from the discretised Zakharov equation, and thus without restriction on spectral…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Given a piecewise $C^{1+\beta}$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and…
We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with full Julia set. If a system is mean stable, then the…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
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…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
The article presents a compact review of the analytical results (2002-2009) in the study of the system describing the motion of a top in two constant fields. The Liouville integrability of this system under certain condition of the…
As low-thrust space missions increase in prevalence, it is becoming increasingly important to design robust trajectories against unforeseen thruster outages or missed thrust events. Accounting for such events is particularly important in…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…