We show that for every “locally finite” unit-preserving completely positive map P acting on a C∗-algebra, there is a corresponding ∗-automorphism α of another unital C∗-algebra such that the two sequences P, P , P , . . . and α,α, α, . . . have the same asymptotic behavior. The automorphism α is uniquely determined by P up to conjugacy. Similar results hold for normal completely positive maps o...

We consider suspension semi-flows of angle-multiplying maps on the circle. Under a Cgeneric condition on the ceiling function, we show that there exists an anisotropic Sobolev space[3] contained in the L space such that the Perron-Frobenius operator for the time-t-map acts on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum exp...

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F . Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F . This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron–Frobenius or...

We construct center-stable and center-unstable manifolds, as well as stable and unstable manifolds, for the nonlinear Klein–Gordon equation with a focusing energy subcritical nonlinearity, associated with a family of solitary waves which is generated from any radial stationary solution by the action of all Lorentz transforms and spatial translations. The construction is based on the graph trans...

Let A be a nonnegative square matrix whose symmetric part has rank one. Tournament matrices are of this type up to a positive shift by 1/2I . When the symmetric part of A is irreducible, the Perron value and the left and right Perron vectors of L(A, α) = (1 − α)A+ αAt are studied and compared as functions of α ∈ [0, 1/2]. In particular, upper bounds are obtained for both the Perron value and it...

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...

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