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.
Original language | English |
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Pages (from-to) | 393-407 |
Number of pages | 15 |
Journal | Transactions of the American Mathematical Society |
Volume | 289 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 1985 |
Externally published | Yes |
Keywords
- Compact group
- Ergodic semigroup
- Invariant set
- Semigroup of affine transformations
- Semigroup of epimorphisms
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics