linoleon

Linoleon is a fictional construct used in mathematical thought experiments to illustrate how linear and nonlinear components can interact within dynamical systems. In the fictional framework, a linoleon is modeled on a finite-dimensional real vector space V, and its action is described by a map L: V → V that decomposes into a linear part and a nonlinear part. A common representation is L(v) = Av + f(v), where A is a linear operator on V and f: V → V is a nonlinear perturbation bounded in norm by a small parameter ε, chosen to preserve certain invariants of the linear part.

The term linoleon is a neologism formed from “linear” and “neologism,” reflecting its status as a constructed concept for teaching and exploration rather than a standard object in established theory.

History of its use is limited to online lecture notes and forum discussions since the early 2010s, where it is employed as a didactic device to discuss perturbation theory, stability, and invariant sets. It is not part of a formal, widely accepted body of mathematical literature, and references to linoleon vary in detail and rigor.

Applications in educational contexts emphasize comparing linear predictions with nonlinear behavior, demonstrating how small nonlinear terms can alter fixed points, basins of attraction, and bifurcation structure. It is often presented alongside linearization, normal form theory, and simple nonlinear maps to highlight the limits of linear analyses and to foster intuition about nonlinear dynamical phenomena.

See also: Linearization; Nonlinear dynamics; Dynamical systems; Perturbation theory.