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I'm in my final year of my undergraduate studies doing work on modelling the n-body problem numerically and I also have some interest in theoretical guarantees. Now, I've been looking for a theorem that guarantees the following:

$$\text{KAM stable} \implies \text{smooth orbits} \tag{*}$$

To be precise I mean that if we decompose a KAM stable solution to the n-body problem into n closed curves(not necessarily distinct) then each of these curves must be smooth. I haven't come across such a theorem so far but I'm certain it must be true.

Note 1: I haven't read all the literature on KAM theory but I've read a few introductions on the subject(ex. Jacques Fejoz).

Note 2: Smoothness would rule out collision or non-collision singularities but it doesn't imply KAM stability as there are smooth orbits which aren't KAM stable. Ex: all solutions to the three body problem besides the figure eight solution. So the converse is obviously false.

I'm in my final year of my undergraduate studies doing work on modelling the n-body problem numerically and I also have some interest in theoretical guarantees. Now, I've been looking for a theorem that guarantees the following:

$$\text{KAM stable} \implies \text{smooth orbits} \tag{*}$$

To be precise I mean that if we decompose a KAM stable solution to the n-body problem into n curves(not necessarily distinct) then each of these curves must be smooth. I haven't come across such a theorem so far but I'm certain it must be true.

Note 1: I haven't read all the literature on KAM theory but I've read a few introductions on the subject(ex. Jacques Fejoz).

Note 2: Smoothness would rule out collision or non-collision singularities but it doesn't imply KAM stability as there are smooth orbits which aren't KAM stable. Ex: all solutions to the three body problem besides the figure eight solution. So the converse is obviously false.

I'm in my final year of my undergraduate studies doing work on modelling the n-body problem numerically and I also have some interest in theoretical guarantees. Now, I've been looking for a theorem that guarantees the following:

$$\text{KAM stable} \implies \text{smooth orbits} \tag{*}$$

I haven't come across such a theorem so far but I'm certain it must be true.

Note 1: I haven't read all the literature on KAM theory but I've read a few introductions on the subject(ex. Jacques Fejoz).

Note 2: Smoothness would rule out collision or non-collision singularities but it doesn't imply KAM stability as there are smooth orbits which aren't KAM stable. Ex: all solutions to the three body problem besides the figure eight solution. So the converse is obviously false.

I'm in my final year of my undergraduate studies doing work on modelling the n-body problem numerically and I also have some interest in theoretical guarantees. Now, I've been looking for a theorem that guarantees the following:

$$\text{KAM stable} \implies \text{smooth orbits} \tag{*}$$

To be precise I mean that if we decompose a KAM stable solution to the n-body problem into n closed curves(not necessarily distinct) then each of these curves must be smooth. I haven't come across such a theorem so far but I'm certain it must be true.

Note 1: I haven't read all the literature on KAM theory but I've read a few introductions on the subject(ex. Jacques Fejoz).

Note 2: Smoothness would rule out collision or non-collision singularities but it doesn't imply KAM stability as there are smooth orbits which aren't KAM stable. Ex: all solutions to the three body problem besides the figure eight solution. So the converse is obviously false.

I'm in my final year of my undergraduate studies doing work on modelling the n-body problem numerically and I also have some interest in theoretical guarantees. Now, I've been looking for a theorem that guarantees the following:

$$\text{KAM stable} \implies \text{smooth trajectories} \tag{*}$$

I haven't come across such a theorem so far but I'm certain it must be true.

Note 1: I haven't read all the literature on KAM theory but I've read a few introductions on the subject(ex. Jacques Fejoz).

Note 2: Smoothness would rule out collision or non-collision singularities but it doesn't imply KAM stability as there are smooth trajectories which aren't KAM stable. Ex: all solutions to the three body problem besides the figure eight solution. So the converse is obviously false.

I'm in my final year of my undergraduate studies doing work on modelling the n-body problem numerically and I also have some interest in theoretical guarantees. Now, I've been looking for a theorem that guarantees the following:

$$\text{KAM stable} \implies \text{smooth orbits} \tag{*}$$

I haven't come across such a theorem so far but I'm certain it must be true.

Note 1: I haven't read all the literature on KAM theory but I've read a few introductions on the subject(ex. Jacques Fejoz).

Note 2: Smoothness would rule out collision or non-collision singularities but it doesn't imply KAM stability as there are smooth orbits which aren't KAM stable. Ex: all solutions to the three body problem besides the figure eight solution. So the converse is obviously false.