proof of Poincaré recurrence theorem 2
Let be a basis of open sets for , and for each define
From theorem 1 we know that . Let Then . We assert that if then is recurrent. In fact, given a neighborhood of , there is a basic neighborhood such that , and since we have that which by definition of means that there exists such that ; thus is recurrent.
|Title||proof of Poincaré recurrence theorem 2|
|Date of creation||2013-03-22 14:29:58|
|Last modified on||2013-03-22 14:29:58|
|Last modified by||Koro (127)|