Timeline for Does a smooth dynamical system always come with a metric
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Feb 24, 2018 at 22:59 | review | Close votes | |||
| Mar 20, 2018 at 3:03 | |||||
| Feb 6, 2018 at 22:14 | comment | added | Willie Wong | Ok, let me try to reformulate what you wrote to see if I understand your question. You are given a dynamical system and you are interested in whether the system induces a sort of metric on an arbitrary (?) invariant submanifold of your system. Is that more-or-less correct? There's something I still don't understand: if you are just interested in an invariant manifold $M$, there is no guarantee that given any arbitrary $y, z\in M$ that they belong to the same orbit. What would the distance between them in this case? | |
| Feb 6, 2018 at 3:26 | comment | added | Sujaan | @WillieWong Thanks for the comment. Yes, I am particularly interested in differential equations but didn't want the question to sound too specific. I mean the collection describes a smooth manifold. So let's say a torus described by quasiperiodic motion. I am tempted to include strange attractor, but I am not sure about that. | |
| Feb 5, 2018 at 15:53 | comment | added | Piyush Grover | No. Consider a period-2 orbit $y_1\rightarrow y_2 \rightarrow y_1$. It maps points arbitrarily far away to each other in 1 iteration. | |
| Feb 5, 2018 at 15:44 | comment | added | Willie Wong | You tagged differential equations: do you actually mean $\dot{x} = f(x)$ for your dynamical system? If not, do you mean to tag using "difference equations"? For clarification: by the phrase "the trajectories of which describe a smooth manifold in the state space", do you mean that each trajectory describe a smooth manifold, or are you considering the collection of all trajectories as a smooth manifold? | |
| Feb 5, 2018 at 15:00 | review | First posts | |||
| Feb 5, 2018 at 15:09 | |||||
| Feb 5, 2018 at 14:56 | history | asked | Sujaan | CC BY-SA 3.0 |