On Frobenius-Perron dimension

Multiple Perron-Frobenius operators.

A cycle expansion technique for discrete sums of several PF operators, similar to the one used in the standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particular mappings entering the sum.

Stochastic Nonlinear Perron-frobenius Theorem∗

We establish a stochastic nonlinear analogue of the PerronFrobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space (Ω,F , P ) and a random mapping D(ω, ·) : R+ → R+. Under assumptions of monotonicity and homogeneity of D(ω, ·), we prove the existence of scalar and vector measurable functions α(ω) > 0 an...

Weighted Frobenius-Perron and Koopman operators

Perron-Frobenius Theorem for Spectral Radius Analysis

The spectral radius of a matrix A is the maximum norm of all eigenvalues of A. In previous work we already formalized that for a complex matrix A, the values in A grow polynomially in n if and only if the spectral radius is at most one. One problem with the above characterization is the determination of all complex eigenvalues. In case A contains only non-negative real values, a simplification ...

Stochastic Properties of the Frobenius-perron Operator

In the present paper the Renormalization Group (RG) method is adopted as a tool for a constructive analysis of the properties of the Frobenius-Perron Operator. The renormalization group reduction of a generic symplectic map in the case, where the unperturbed rotation frequency of the map is far from structural resonances driven by the kick perturbation has been performed in detail. It is furthe...