Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles

The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite…

The generalized Lefschetz number of homeomorphisms on punctured disks

We compute the generalized Lefschetz number of orientation-preserving self-homeomorphisms of a compact punctured disk, using the fact that homotopy classes of these homeomorphisms can be identified with braids. This result is applied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk. We determine, for a certain class of braids, the rotation number of the corresponding canonical homeomorphisms on the outer boundary circle. Also,it is shown that the canonical homeomorphisms corresponding to some braids are pseudo-Anosov.

广义勒夫谢茨数与环辫群

The generalized Lefschetz number and loop braid groups

本文通过引入环辫群和广义勒夫谢茨数，研究三维流形中同胚的固定点和周期点的拓扑动力学性质。