Concept

Integrable system

Summary
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space. Three features are often referred to as characterizing integrable systems:
  • the existence of a maximal set of conserved quantities (the usual defining property of complete integrability)
  • the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability)
  • the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability)
Integrable systems may be seen as very different in qualitative character from more generic dynamical systems, which are more typically chaotic systems. The latt
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