= 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).
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