protoplanetary disc shredded by 3 central stars

[turboscrew]

The path of the system is arbitrarily close to the attractor.

Arbitrarily close to what?

THAT! You're making this too hard..... Just because the set of points of an orbit is arbitrarily close to the a funny set doesn't mean that the set isn't asymptotically stable.

(Alternating between scratching my head and and removing splinters from under my finger nails...)

[notFritzArgelander]

Arbitrarily close to what?

THAT! You're making this too hard..... Just because the set of points of an orbit is arbitrarily close to the a funny set doesn't mean that the set isn't asymptotically stable.

(Alternating between scratching my head and and removing splinters from under my finger nails...)

Let's try this.... if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?
The answer is yes. Therefore AFAIK the Lorenz attractor is asymptotically stable.

[turboscrew]

THAT! You're making this too hard..... Just because the set of points of an orbit is arbitrarily close to the a funny set doesn't mean that the set isn't asymptotically stable.

(Alternating between scratching my head and and removing splinters from under my finger nails...)

Let's try this.... if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?
The answer is yes. Therefore AFAIK the Lorenz attractor is asymptotically stable.

It's the "asymptotically" that confuses me. That usually means closing in, but never quite reaching something. That's why I guessed it is stable, but not asymptotically. And how does a trajectory get close to "family of curves"? What does it get close to, then?
BTW, "if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?"
Almost poetically put.

[notFritzArgelander]

(Alternating between scratching my head and and removing splinters from under my finger nails...)

Let's try this.... if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?
The answer is yes. Therefore AFAIK the Lorenz attractor is asymptotically stable.

It's the "asymptotically" that confuses me. That usually means closing in, but never quite reaching something. That's why I guessed it is stable, but not asymptotically. And how does a trajectory get close to "family of curves"? What does it get close to, then?
BTW, "if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?"
Almost poetically put.

Ah, that helps. I think we have a resolution.

I think you are overloading the word "asymptotically". The "never quite reaching" is extra. In this case we have asymptotic stability in time. If you delta yourself away, in time you epsilon your way back and that epsilon can be shown to be smaller as time goes by,

[turboscrew]

Let's try this.... if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?
The answer is yes. Therefore AFAIK the Lorenz attractor is asymptotically stable.

It's the "asymptotically" that confuses me. That usually means closing in, but never quite reaching something. That's why I guessed it is stable, but not asymptotically. And how does a trajectory get close to "family of curves"? What does it get close to, then?
BTW, "if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?"
Almost poetically put.

Ah, that helps. I think we have a resolution.

I think you are overloading the word "asymptotically". The "never quite reaching" is extra. In this case we have asymptotic stability in time. If you delta yourself away, in time you epsilon your way back and that epsilon can be shown to be smaller as time goes by,

Yes,,, in TIME!. Now I got it - finally. Thanks for your extreme patience with me, nFA.

[notFritzArgelander]

It's the "asymptotically" that confuses me. That usually means closing in, but never quite reaching something. That's why I guessed it is stable, but not asymptotically. And how does a trajectory get close to "family of curves"? What does it get close to, then?
BTW, "if you delta your system away from its Lorenz orbit will it not epsilon its way back to a Lorenz orbit?"
Almost poetically put.

Ah, that helps. I think we have a resolution.

I think you are overloading the word "asymptotically". The "never quite reaching" is extra. In this case we have asymptotic stability in time. If you delta yourself away, in time you epsilon your way back and that epsilon can be shown to be smaller as time goes by,

Yes,,, in TIME!. Now I got it - finally. Thanks for your extreme patience with me, nFA.

Not a worry. It's always pleasure to talk through a conceptual clarification.