Page "Dynamical system" Paragraph 63

This is known as the conjugation equation.

Finding conditions for this equation to hold has been one of the major tasks of research in dynamical systems.

Poincaré first approached it assuming all functions to be analytic and in the process discovered the non-resonant condition.

If λ < sub > 1 </ sub >, ..., λ < sub > ν </ sub > are the eigenvalues of J they will be resonant if one eigenvalue is an integer linear combination of two or more of the others.

As terms of the form λ < sub > i </ sub > – ∑ ( multiples of other eigenvalues ) occurs in the denominator of the terms for the function h, the non-resonant condition is also known as the small divisor problem.