Dynamical Systems

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11 domain-specific abstractions whose origin domain is Dynamical Systems.

• Carleman linearization — A lifting method that represents a finite-dimensional nonlinear dynamical system as an infinite-dimensional linear system over monomials, then truncates it for approximation.
• Chaotic scattering — Scattering dynamics in which arbitrarily small changes in incoming conditions produce fractal changes in exit channel, angle or delay time.
• Ergodicity — A measure-preserving dynamical property in which every invariant measurable set has measure zero or full measure, making the system statistically indecomposable.
• Hartman–Grobman Theorem — Near a hyperbolic equilibrium or fixed point, a differentiable nonlinear dynamical system is locally topologically conjugate to its linearization, so qualitative orbit structure can be read from the linear model.
• Isochron — Collect initial states that share one asymptotic phase or reduced long-term trajectory, forming a level set of the system's asymptotic-state map across transient directions.
• Kaplan–Yorke map — A two-dimensional skew-product chaotic map coupling the doubling map x↦2x mod 1 to a driven contraction or expansion y↦αy+cos(4πx), with dynamics controlled by one parameter α.
• Linear dynamical system — A dynamical system whose state evolution and output laws are linear, enabling superposition and analysis through matrices, spectra, and modes.
• N-body problem — The problem of determining the coupled motion of multiple bodies interacting through mutual forces, classically Newtonian gravitation.
• Recurrent point — A point of a dynamical system that returns arbitrarily close to itself at arbitrarily late iterates, equivalently belonging to its own omega-limit set.
• Stable manifold — The invariant manifold consisting locally or globally of states whose forward trajectories converge to a hyperbolic fixed point or invariant set, tangent to its stable eigenspace.
• Strange nonchaotic attractor — An invariant attracting set with geometrically nonsmooth or fractal structure but no positive maximal Lyapunov exponent.