We consider the problem of counting simultaneous conjugacy classes n-tuples in a finite group G. Let αG,n denote number n-tuples, and βG,n commuting study generating functions AG(t)=∑n≥0αG,ntn, BG(t)=∑n≥0βG,ntn, which are rational t. show that AG(t) determines is completely determined by class equation prove normalized AG(t/|G|) BG(t/|G|) invariants isoclinism families. compute exponential grow...

This note presents the study of the conjugacy classes of elements of some given finite order n in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if n is even, n = 3 or n = 5, and that it is equal to 3 (respectively 9) if n = 9 (respectively 15), and is exactly 1 for all remaining odd orders. Some precise representative elements of the...

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...