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The stability problem for transformations of the circle

Published online by Cambridge University Press:  14 November 2011

Douglas Cenzer
Douglas Cenzer
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611, U.S.A.
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Synopsis

Let I be the group of rotations of the circle and suppose that a map f from I into I is “almost linear”. More precisely, let ε be a positive real number and suppose that d(f(x)+f(y), f(x + y))<ε for all x and y in I; f is said to be an ε-homomorphism. If ε is sufficiently small, then a homomorphism h from I into I can be constructed such that d(f(x), h(x))≦ε for all x in I. This result is refined and generalized in several ways.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 3-4 , 1979 , pp. 279 - 281
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

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