I am familiar with the existence and uniqueness of solutions to the system(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \dot{x} = f(x) [/tex]

requiring [tex]f(x)[/tex] to be Lipschitz continuous, but I am wondering what the conditions are for the system

[tex] \dot{q}(x) = f(x) [/tex].

It seems like I could make the same argument for there existing a unique [tex]q(x)[/tex] provided [tex]f(x)[/tex] is Lipschitz with respect to [tex]q(x)[/tex]. Then if [tex]q(x)[/tex] is invertible or one-to-one or whatever the proper math term is, then I can get a unique [tex]x[/tex]. Is that correct? If that's the case it looks like I'm just doing a nonlinear change of coordinates, showing uniqueness in that coordinate system, and then having a unique map back to the original coordinate system.

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# Existence and Uniqueness

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