Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ergodic semigroups of epimorphisms

Author: Daniel Berend
Journal: Trans. Amer. Math. Soc. 289 (1985), 393-407
MSC: Primary 22D40; Secondary 54H15, 54H20
MathSciNet review: 779072
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Abstract: The conditions for ergodicity of semigroups of epimorphisms of compact groups are studied. In certain cases ergodic semigroups are shown to contain small ergodic subsemigroups. Properties related to ergodicity, such as that of admitting no infinite closed invariant proper subset of the group, are discussed for semigroups of epimorphisms and of affine transformations.

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Keywords: Ergodic semigroup, semigroup of epimorphisms, semigroup of affine transformations, compact group, invariant set
Article copyright: © Copyright 1985 American Mathematical Society