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Outputs (65)

Entropy and the canonical height (2001)
Journal Article
Einsiedler, M., Everest, G., & Ward, T. (2001). Entropy and the canonical height. Journal of Number Theory, 91(2), 256-273. https://doi.org/10.1006/jnth.2001.2682

The height of an algebraic number in the sense of Diophantine geometry is a measure of arithmetic complexity. There is a well-known relationship between the entropy of automorphisms of solenoids and classical heights. We consider an elliptic analogue... Read More about Entropy and the canonical height.

Expansive subdynamics for algebraic Z^d-actions (2001)
Journal Article
Einsiedler, M., Lind, D., Miles, R., & Ward, T. (2001). Expansive subdynamics for algebraic Z^d-actions. Ergodic Theory and Dynamical Systems, 21(6), 1695-1729. https://doi.org/10.1017/s014338570100181x

A general framework for investigating topological actions of Z^d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of R^d. Here we completely describe this expansive behavior for... Read More about Expansive subdynamics for algebraic Z^d-actions.

Primes in divisibility sequences (2001)
Journal Article
Everest, G., & Ward, T. (2001). Primes in divisibility sequences. Cubo (Temuco. Print), 3(2), 245-259

We give an overview of two important families of divisibility sequences: the Lehmer--Pierce family (which generalise the Mersenne sequence) and the elliptic divisibility sequences. Recent computational work is described, as well as some of the mathem... Read More about Primes in divisibility sequences.

Primes in elliptic divisibility sequences (2001)
Journal Article
Einsiedler, M., Everest, G., & Ward, T. (2001). Primes in elliptic divisibility sequences. LMS journal of computation and mathematics, 4, 1-13. https://doi.org/10.1112/s1461157000000772

Morgan Ward pursued the study of elliptic divisibility sequences initiated by Lucas, and Chudnovsky and Chudnovsky suggested looking at elliptic divisibility sequences for prime appearance. The problem of prime appearance in these sequences is examin... Read More about Primes in elliptic divisibility sequences.

A dynamical property unique to the Lucas sequence (2001)
Journal Article
Puri, Y., & Ward, T. (2001). A dynamical property unique to the Lucas sequence. The Fibonacci quarterly, 39(5), 398-402

The only recurrence sequence satisfying the Fibonacci recurrence and realizable as the number of periodic points of a map is (a multiple of) the Lucas sequence.

The canonical height of an algebraic point on an elliptic curve (2000)
Journal Article
Everest, G., & Ward, T. (2000). The canonical height of an algebraic point on an elliptic curve. New York journal of mathematics, 6, 331-342

We use elliptic divisibility sequences to describe a method for estimating the global canonical height of an algebraic point on an elliptic curve. This method requires almost no knowledge of the number field or the curve, is simple to implement, and... Read More about The canonical height of an algebraic point on an elliptic curve.

Fitting ideals for finitely presented algebraic dynamical systems (2000)
Journal Article
Einsiedler, M., & Ward, T. (2000). Fitting ideals for finitely presented algebraic dynamical systems. Aequationes Mathematicae, 60(1-2), 57-71. https://doi.org/10.1007/s000100050135

We consider a class of algebraic dynamical systems introduced by Kitchens and Schmidt. Under a weak finiteness condition - the Descending Chain Condition - the dual modules have finite resentations. Using methods from commutative algebra we show how... Read More about Fitting ideals for finitely presented algebraic dynamical systems.

Primes in sequences associated to polynomials (after Lehmer) (2000)
Journal Article
Einsiedler, M., Everest, G., & Ward, T. (2000). Primes in sequences associated to polynomials (after Lehmer). LMS journal of computation and mathematics, 3, 125-139. https://doi.org/10.1112/s1461157000000255

In a paper of 1933, D.H. Lehmer continued Pierce's study of integral sequences associated to polynomials, generalizing the Mersenne sequence. He developed divisibility criteria, and suggested that prime apparition in these sequences -- or in closely... Read More about Primes in sequences associated to polynomials (after Lehmer).

Dynamical systems arising from elliptic curves (2000)
Journal Article
D'Ambros, P., Everest, G., Miles, R., & Ward, T. (2000). Dynamical systems arising from elliptic curves. Colloquium Mathematicum, 84/85(1), 95-107

We exhibit a family of dynamical systems arising from rational points on elliptic curves in an attempt to mimic the familiar toral automorphisms. At the non-archimedean primes, a continuous map is constructed on the local elliptic curve whose topolog... Read More about Dynamical systems arising from elliptic curves.