- #1
Eidos
- 108
- 1
Hello ladies and gentlemen
Why can't flows in phase space cross?
Would it imply that the system may be at the same state at some future time and then follow a different trajectory? That is to say that the identical initial condition gives a different final condition.
To my mind, flows in phase space would only not cross if the system is time invariant.
Slightly related, non-dissipative systems have their volumes preserved in phase space (Liouville's Theorem), is that the total volume of the phase space or any selectable portion of it?
Thanks for any replies![Smile :smile: :smile:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Why can't flows in phase space cross?
Would it imply that the system may be at the same state at some future time and then follow a different trajectory? That is to say that the identical initial condition gives a different final condition.
To my mind, flows in phase space would only not cross if the system is time invariant.
Slightly related, non-dissipative systems have their volumes preserved in phase space (Liouville's Theorem), is that the total volume of the phase space or any selectable portion of it?
Thanks for any replies