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Perron-Frobenius Operator

An operator which describes the time evolution of densities in phase space. The operator can be defined by

rho_(n+1)=L^~rho_n,

where rho_n are the natural invariants after the nth iteration of a map f. This can be explicitly written as

L^~rho(y)=sum_(x in f^(-1)(y))(rho(x))/(|f^'(x)|).

See also

Frobenius-Perron Equation

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References

Berman, A. and Plemmons, R. Nonnegative Matrices in the Mathematical Sciences. New York: Academic Press, 1979.Beck, C. and Schlögl, F. "Transfer Operator Methods." Ch. 17 in Thermodynamics of Chaotic Systems. Cambridge, England: Cambridge University Press, pp. 190-203, 1995.

Referenced on Wolfram|Alpha

Perron-Frobenius Operator

Cite this as:

Weisstein, Eric W. "Perron-Frobenius Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Perron-FrobeniusOperator.html

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