Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...

We propose behavioral specification theories for most equivalences in the linear-time–branching-time spectrum. Almost all previous work on specification theories focuses on bisimilarity, but there is a clear interest in specification theories for other preorders and equivalences. We show that specification theories for preorders cannot exist and develop a general scheme which allows us to defin...

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...

In particular, (6) implies that the functions/i, • • • , /„ are all regular in the domain (7) a > 0, i wi\ < r, • • • ,| to„| < r. In these notations, the following theorem will be proved: Theorem. In the domain (7), let fx, • ■ • ,fnbe regular functions of the form (1) with uniformly almost periodic coefficient functions defined on (2) having Fourier expansions of the type (3), satisfying (4)....

We show that a completely multiplicative automatic function, which dos not have 0 as value, is almost periodic.

This paper studies some sufficient conditions for the existence and uniqueness of a pseudo almost periodic mild solution to abstract hyperbolic differential equations with infinite delay. Applications include the existence and uniqueness of a pseudo almost periodic mild solution to the heat equation.

L is a continuous function from R× into X and f is a continuous function from R to X . The theory of functional differential equations with infinite delay has been developed by several authors. The fundamental task of that kind of equations is the choice of phase space . Since the history function t→ ut is not continuous in general if u : (−∞,T] → X is continuous (where T > 0). The paper [9] co...