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Journal of the London Mathematical Society 1995 52(3):497-516; doi:10.1112/jlms/52.3.497
© 1995 by London Mathematical Society
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© The London Mathematical Society

A Skew Product Entropy for Nonsingular Transformations

Cesar E. Silva and Philippe Thieullen

Department of Mathematics, Williams College Williamstown, Massachusetts 01267, USA
Université Paris-Sud, Département de Mathématiques 91405 Orsay Cedex, France

Received 3 February 1994. Revision received 1 June 1994.

We define a skew product entropy for conservative nonsingular transformations, show that it takes values in {0, {infty}} and use it to distinguish two classes on nonsingular transformations. Binary and ternary type III{lambda} odometers have zero skew product entropy, while nonsingular K-automorphisms have infinite skew product entropy.

The first author was partially supported by NSF grants DMS90-02875 and DMS92-14077.


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