The Library
On zeta functions and Anosov diffeomorphisms
Tools
Tools
Tools
Manning, Anthony (1972) On zeta functions and Anosov diffeomorphisms. PhD thesis, University of Warwick.
|
PDF
WRAP_Thesis_Manning_1972.pdf - Requires a PDF viewer. Download (1761Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b1735723~S1
Abstract
This thesis considers some problems in Dynamical Systems concerned with zeta functions and with Anosov diffeomorphisms.
In chapter 1 Bowen's method of expressing a basic set of an Axiom A diffeomorphism as a quotient of a subshift of finite type is used ,to calculate the numbers of periodic points of the diffeomorphism and show that its zeta function is ration31 which gives an affirmative answer to a question of Smale.
The rest of the thesis is concerned with Anosov diffeomorphisms of nilmanifolds.Chapter 2 contains some facts about nilmanifolds describing them as
twisted products of tori. Anilmanifold has a maximal torus factor. A hyperbolic nilmanifold automorphism projects onto an automorphism of this torus and we , say it has the toral automorphism as a factor.
In chapter 3 we generalize this situation to show that many diffeomorphisms of other manifolds have toral automorphisms as factors and give some examples.
In the last chapter we use a spectral sequence associated to another decomposition of a nilrnanifold into tori to calculate the Lefschetz number of any diffeomorphism of the nilmanifold. This enables us to prove a necessary condition on the map induced by an Anosov, diffeomorphism of a nilmanifold on its fundamental group. Then we consider the question of finding hyperbolic automorphisms of nilmanifolds from the decomposition into tori. Fin311y we calculate the zeta function of such an automorphism.
| Item Type: | Thesis or Dissertation (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Differentiable dynamical systems, Functions, Zeta, Diffeomorphisms | ||||
| Official Date: | June 1972 | ||||
| Dates: |
|
||||
| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Bowen, R. ; Zeeman, E. C. (Erik Christopher), 1925- | ||||
| Sponsors: | Science Research Council (Great Britain) | ||||
| Extent: | 56 leaves | ||||
| Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
