The s-Perron, sap-Perron and ap-McShane Integrals

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.

The smallest Perron numbers

A Perron number is a real algebraic integer α of degree d ≥ 2, whose conjugates are αi, such that α > max2≤i≤d |αi|. In this paper we compute the smallest Perron numbers of degree d ≤ 24 and verify that they all satisfy the Lind-Boyd conjecture. Moreover, the smallest Perron numbers of degree 17 and 23 give the smallest house for these degrees. The computations use a family of explicit auxiliar...

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.

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))

Spectrum Properties of the Koopman and Frobenius-Perron Operators