Limit Cycle

Nusc

http://books.google.ca/books?id=Pd8-...ed=0CAkQ6AEwAA

Let ~ denote vector.
For a fixed point.
(~x0 is asymptotically stable if there exists
a neighbourhood U of ~x0 such that if ~x(t) obeys Hamilton's equations and ~x(0) in U, then lim
t->inf
~x(t) = ~x0.)

can you give me a precise definition for periodic solutions (limit cycles) in this context?

Eynstone

Quote by Nusc

http://books.google.ca/books?id=Pd8-...ed=0CAkQ6AEwAA

Let ~ denote vector.
For a fixed point.
(~x0 is asymptotically stable if there exists
a neighbourhood U of ~x0 such that if ~x(t) obeys Hamilton's equations and ~x(0) in U, then lim
t->inf
~x(t) = ~x0.)

can you give me a precise definition for periodic solutions (limit cycles) in this context?

A solution x is periodic iff there exists T >0 with x(t+T) = x(t) for all t.

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Nusc	Limit Cycle Tweet http://books.google.ca/books?id=Pd8-...ed=0CAkQ6AEwAA Let ~ denote vector. For a fixed point. (~x0 is asymptotically stable if there exists a neighbourhood U of ~x0 such that if ~x(t) obeys Hamilton's equations and ~x(0) in U, then lim t->inf ~x(t) = ~x0.) can you give me a precise definition for periodic solutions (limit cycles) in this context?