Skip to main content

Research Repository

Advanced Search

Outputs (80)

Algebraic and Topological Dynamics (2005)
Presentation / Conference Contribution
Kolyada, S., Manin, Y., & Ward, T. (2005, December). Algebraic and Topological Dynamics. Presented at Special program on algebraic and topological dynamics, Max-Planck Institute, Bonn, Germany

Entropy geometry and disjointness for zero-dimensional algebraic actions (2005)
Journal Article
Einsiedler, M., & Ward, T. (2005). Entropy geometry and disjointness for zero-dimensional algebraic actions. Journal für die reine und angewandte Mathematik, 584, 195-214. https://doi.org/10.1515/crll.2005.2005.584.195

We show that many algebraic actions of higher-rank abelian groups on zero-dimensional compact abelian groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and a form of Abramov-Rokhlin formula... Read More about Entropy geometry and disjointness for zero-dimensional algebraic actions.

Finite entropy characterizes topological rigidity on connected groups (2005)
Journal Article
Bhattacharya, S., & Ward, T. (2005). Finite entropy characterizes topological rigidity on connected groups. Ergodic Theory and Dynamical Systems, 25(2), 365-373. https://doi.org/10.1017/s0143385704000501

Let X, Y be mixing connected algebraic dynamical systems with the Descending Chain Condition. We show that every equivariant continuous map from X to Y is affine (that is, Y is topologically rigid) if and only if the system Y has finite topological e... Read More about Finite entropy characterizes topological rigidity on connected groups.

Isomorphism rigidity in entropy rank two (2005)
Journal Article
Einsiedler, M., & Ward, T. (2005). Isomorphism rigidity in entropy rank two. Israel Journal of Mathematics, 147(1), 269-284. https://doi.org/10.1007/bf02785368

We study the rigidity properties of a class of algebraic Z^3-actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show isomorphism rigidity... Read More about Isomorphism rigidity in entropy rank two.

An Introduction to Number Theory (2005)
Book
Everest, G., & Ward, T. (2005). An Introduction to Number Theory. Springer Verlag

An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate h... Read More about An Introduction to Number Theory.

Morphic heights and periodic points (2004)
Book Chapter
Einsiedler, M., Everest, G., & Ward, T. (2004). Morphic heights and periodic points. In D. Chudnovsky, G. Chudnovsky, & M. Nathanson (Eds.), Number theory : New York seminar 2003 (167-177). Springer Verlag

An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic height is expre... Read More about Morphic heights and periodic points.

Asymptotic geometry of non-mixing sequences (2003)
Journal Article
Einsiedler, M., & Ward, T. (2003). Asymptotic geometry of non-mixing sequences. Ergodic Theory and Dynamical Systems, 23(1), 75-85. https://doi.org/10.1017/s0143385702000950

The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here we use valuations in function fields to exhibit an asymptotic shape in non-mixing sequences for algebraic Z^2-actions. This gives a relationsh... Read More about Asymptotic geometry of non-mixing sequences.