Let G be a locally compact σ -compact group with right Haar measure λ. A sequence {μn} of probabilities on G is called ergodic if for every f ∈ L1(G, λ) and t ∈ G we have ‖μn* (f − δt* f) ‖1 → 0. If T (t) is a bounded continuous representation of G by linear operators in a Banach space X, we define the μ,-average of T(t) by .

We consider a compound central field in the Euclidean plane which is governed by a finite number of bell-shaped potential functions with finite range. The study of the qualitative behavior of the Hamilton flow in such a potential field can be reduced to that of the so-called perturbed billiards system. The main result in this paper is the construction of a symbolic dynamics of the Hamilton flow by using the perturbed billiards system provided that the energy E > 0 is small enough. We also try to show an analogue of the prime number theorem for the closed orbits of the flow following ideas presented by Morita and Parry and Pollicott.

Let T be a measure-preserving transformation of the Lebesgue probability space (X, F, μ). We call (X, Fμ, T) a dynamical system. Bourgain has proven the following theorem.

Due to an editorial omission the full acknowledgments to Maria Carvalho's paper Sinai-Ruelle-Bowen measures for N-dimensional derived from Anosov diffeomorphisms (Volume 13: issue 1, p. 44) was not printed. These missing lines are printed below.

Acknowledgment. I was most fortunate to have Professor Ricardo Mané as my PhD supervisor. I am grateful to him for bringing me to this subject, his invaluable guidance and encouragement. I am also thankful to L. Diaz, J. Rocha and M. Viana for helpful discussions.