If the set on the right is empty, then we define . The PoincarÃ© recurrence theorem asserts that is finite for almost every . We define the following sets:
By PoincarÃ© recurrence theorem, . Kac’s theorem asserts that the function is integrable and
When the system is ergodic, then , and Kac’s theorem implies:
This equality can be interpreted as: the mean return time to s inversely proportional to the measure of .
|Date of creation||2014-03-19 22:18:04|
|Last modified on||2014-03-19 22:18:04|
|Last modified by||Filipe (28191)|
|Related topic||PoincarÃ© Recurrence theorem|