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On zeta functions and Anosov diffeomorphisms [PDF]

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 ...
Manning, Anthony
core  

Almost-Bieberbach groups with prime order holonomy

, 1996
The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds.
Dekimpe, Karel, Malfait, Wim
core  

Classification of abelian actions with globally hypoelliptic orbitwise laplacian I [Elektronisk resurs] : The Greenfield-Wallach conjecture on nilmanifolds

For a Rk−action generated by vector fields X1,...,Xk we define an operator −(X12 + ... + Xk2), the orbitwise laplacian. In this paper, we study and classify Rk−actions whose orbitwise laplacian is globally hypoelliptic (GH).
Sandfeldt, Sven,
core  

Classification of abelian actions with globally hypoelliptic orbitwise laplacian I : The Greenfield-Wallach conjecture on nilmanifolds

For a Rk−action generated by vector fields X1,...,Xk we define an operator −(X12 + ... + Xk2), the orbitwise laplacian. In this paper, we study and classify Rk−actions whose orbitwise laplacian is globally hypoelliptic (GH).
Sandfeldt, Sven
core  

On eta-functions for nilmanifolds

, 2014
openaire   +1 more source

Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms

Discrete and Continuous Dynamical Systems, 2016
In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic.
Jonas Dere
exaly   +2 more sources

Central idempotent measures on a nilmanifold

Journal of Functional Analysis, 1980
A characterization of the central idempotent measures on a nilmanifold which generalizes the results of Rudin and Cohen for locally compact Abelian groups is proved.
Richard Penney
exaly   +2 more sources

Free actions of finite groups on the 3-dimensional nilmanifold

Topology and Its Applications, 2004
We study free actions of finite groups on the standard 3-dimensional nilmanifold. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying normal nilpotent subgroups of all almost Bieberbach groups of finite index,
Shin, Joonkook, Hahng Yun Chu, Joonkook Shin, Chu, Hahng Yun   +3 more
exaly   +2 more sources

Stable Lyapunov Spectrum Rigidity of Nilmanifold Endomorphisms

Journal of Dynamics and Differential Equations
Under some non-invertibility and irreducibility condition, for nilmanifold Anosov maps with one-dimensional stable bundle, we get the equivalence among the existence of invariant unstable bundle, the existence of topological conjugacy to its linear part,
Wenchao Li
exaly   +2 more sources

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AFFINE STRUCTURES ON NILMANIFOLDS

International Journal of Mathematics, 1996
We investigate the existence of affine structures on nilmanifolds Γ\G in the case where the Lie algebra g of the Lie group G is filiform nilpotent of dimension less or equal to 11. Here we obtain examples of nilmanifolds without any affine structure in dimensions 10, 11. These are new counterexamples to the Milnor conjecture.
openaire   +2 more sources