Perron transforms and Hironaka's game

Hadamard and Perron JWR

On page 23 of his famous monograph [2], D. V. Anosov writes Every five years or so, if not more often, someone 'discovers' the theorem of Hadamard and Perron proving it either by Hadamard's method or Perron's. I myself have been guilty of this. If (X, d X) and (Y, d Y) are metric spaces and T : X → Y is a map then the Lipschitz constant of T is the quantity lip(T) = sup d Y (T (x 1), T (x 2))

Weighted Frobenius-Perron and Koopman operators

The Strong Perron Integral

In this paper, we study the strong Perron integral, and show that the strong Perron integral is equivalent to the McShane integral.

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.

Spectrum Properties of the Koopman and Frobenius-Perron Operators