Necessary and sufficient conditions for a Lorenz map to be topologically conjugate to a piecewise linear map with constant slope (a β-transformation) are given, first in terms of kneading invariants of the maps and then in terms of the topological entropy restricted to basic sets. The dynamics of β-transformations is also described.

Volume 104 (1988), 1–6

‘On generalized albanese varieties for surfaces’

Hurşit Önsiper

Department of Mathematics, Middle East Technical University, Ankara, Turkey

Theorem 3 of the paper is incorrect. Even when U = X, so that m = 0 and Gum = Albx, it is well known that if and only if the Néron–Severi scheme NS(X) has no torsion. Moreover, the elementary observations in Lemma 1 below show that in characteristic zero for the study of we can replace simply by Gsa. As this lemma is not true in characteristic p, it is essential to consider in this case.