New directions in Nielsen-Reidemeister theory

The Nielsen and the Reidemeister numbers of maps on infra-solvmanifolds of type (R)

We prove the rationality, the functional equations and calculate the radii of convergence of the Nielsen and the Reidemeister zeta functions of continuous maps on infra-solvmanifolds of type $\R$. We find a connection between the Reidemeister and Nielsen zeta functions and the Reidemeister torsions of the corresponding mapping tori. We show that if the Reidemeister zeta function is defined for a homeomorphism on an infra-solvmanifold of type $\R$, then this manifold is an infra-nilmanifold. We also prove that a map on an infra-solvmanifold of type $\R$ induced by an affine map minimizes the to…

Reidemeister 和 Nielsen 数：增长速率、渐进行为、动力学ζ函数和高斯同余

The Reidemeister and the Nielsen numbers: growth rate, asymptotic behavior, dynamical zeta functions and the Gauss congruences

本文从动力学角度研究Reidemeister和Nielsen数序列的增长速率、渐进行为及高斯同余，证明了相关ζ函数的有理性和序列的生长特性。