On the Lefschetz zeta function for quasi-unipotent maps on then-dimensional torus
| Autor: | Víctor F. Sirvent, Pedro Berrizbeitia |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Pure mathematics Algebra and Number Theory Root of unity Mathematics::Number Theory Applied Mathematics Unipotent Mathematics::Geometric Topology Arithmetic zeta function Mathematics::Algebraic Geometry Lefschetz zeta function Arithmetic function Lefschetz fixed-point theorem Mathematics::Representation Theory Mathematics::Symplectic Geometry Cyclotomic polynomial Analysis Mathematics Characteristic polynomial |
| Zdroj: | Journal of Difference Equations and Applications. 20:961-972 |
| ISSN: | 1563-5120 1023-6198 |
| DOI: | 10.1080/10236198.2013.872637 |
| Popis: | We compute the Lefschetz zeta function for quasi-unipotent maps on the n-dimensional torus, using arithmetical properties of the number n. In particular we compute the Lefschetz zeta function for quasi-unipotent maps, such that the characteristic polynomial of the induced map on the first homology group is the th cyclotomic polynomial, when is an odd prime. These computations involve fine combinatorial properties of roots of unity. We also show that the Lefchetz zeta functions for quasi-unipotent maps on are rational functions of total degree zero. We use these results in order to characterized the minimal set of Lefschetz periods for quasi-unipotent maps on , having finitely many periodic points all of them hyperbolic. Among this class of maps are the Morse–Smale diffeomorphisms of . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|