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Lyapunov Exponents

Mathematical quantities describing the rate of divergence or convergence of solutions to dynamical systems, used to analyze the evolution of the inflaton field.
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The statement of the theorem

Consider the linearized perturbation equations for the inflaton field ϕ\phi in an expanding background. The evolution of the perturbation δϕ\delta\phi is governed by a second-order differential equation. The Lyapunov exponents λ\lambda are defined by the asymptotic growth rate of the perturbation δϕ(t)\delta\phi(t): λ=lim⁡t→∞1tln⁡∣δϕ(t)δϕ(t0)∣\lambda = \lim_{t \to \infty} \frac{1}{t} \ln \left| \frac{\delta\phi(t)}{\delta\phi(t_0)} \right| For a general dynamical system defined by x˙=F(x,t)\dot{\mathbf{x}} = \mathbf{F}(\mathbf{x}, t), the exponents are found by analyzing the eigenvalues of the Jacobian matrix J=∂F∂x\mathbf{J} = \frac{\partial \mathbf{F}}{\partial \mathbf{x}} evaluated along the trajectory, quantifying the exponential divergence of nearby trajectories.
Source: Wikipedia