Source: wikibot/exponential-dichotomy

= Exponential dichotomy
{wiki=Exponential_dichotomy}

Exponential dichotomy is a concept from the theory of dynamical systems and differential equations, particularly in the study of linear systems. It describes the behavior of solutions to a linear differential equation in terms of their growth or decay rates over time. \#\#\# Definition An exponential dichotomy occurs for a linear system of the form: \\\[ \\frac\{dx\}\{dt\} = Ax(t) \\\] where \\( A \\) is a linear operator (often represented by a matrix in finite dimensions).