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Integral automorphism

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The same as a special automorphism, constructed from an automorphism of a measure space and a function (given on this space and taking values in the positive integers). The term "integral automorphism" is mostly used in the non-Soviet literature.


Comments

Let be the measure space with measure

Then the integral automorphism corresponding to and is the automorphism of defined by if , and if . For more details see [a1] and Special automorphism.

References

[a1] I.P. [I.P. Kornfel'd] Cornfel'd, S.V. Fomin, Ya.G. Sinai, "Ergodic theory" , Springer (1982) pp. Chapt. 1, Sect. 5 (Translated from Russian)
How to Cite This Entry:
Integral automorphism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_automorphism&oldid=47365
This article was adapted from an original article by D.V. Anosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article