A dynamical interpretation of the global canonical height on an elliptic curve

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Ward, T. and Everest, G. (1998) A dynamical interpretation of the global canonical height on an elliptic curve. Experimental Mathematics, 7 (4). pp. 315-326. ISSN 1944-950X

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Abstract

There is a well-understood connection between polynomials and certain simple algebraic dynamical systems. In this connection, the Mahler measure corresponds to the topological entropy, Kronecker's Theorem relates ergodicity to positivity of entropy, approximants to the Mahler measure are related to growth rates of periodic points, and Lehmer's problem is related to the existence of algebraic models for Bernoulli shifts. There are similar relationships for higher-dimensional algebraic dynamical systems. We review this connection, and indicate a possible analogous connection between the global canonical height attached to points on elliptic curves and a possible ``elliptic'' dynamical system.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
Related URLs:	http://www.ams.org/mathscinet-getitem?mr... http://www.zentralblatt-math.org/zmath/e...
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:48
Last Modified:	15 Dec 2022 02:01
URI:	https://ueaeprints.uea.ac.uk/id/eprint/19293
DOI:

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