The Perron-Frobenius operator is an operator which describes the time evolution of densities in phase space. The operator can be defined by
 |
where 
are the natural invariants after the 
th iteration of a map 
. This can be explicitly written as
 |
Perron-Frobenius Operator
See also
Frobenius-Perron EquationExplore with Wolfram|Alpha
References
Beck, C. and Schlögl, F. "Transfer Operator Methods." Ch. 17 in Thermodynamics of Chaotic Systems. Cambridge, England: Cambridge University Press, pp. 190-203, 1995.Berman, A. and Plemmons, R. Nonnegative Matrices in the Mathematical Sciences. New York: Academic Press, 1979.Referenced on Wolfram|Alpha
Perron-Frobenius OperatorCite this as:
Weisstein, Eric W. "Perron-Frobenius Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Perron-FrobeniusOperator.html