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Smoothness is not an obstruction to realizability

Published online by Cambridge University Press:  01 June 2008

A. J. WINDSOR
A. J. WINDSOR*
Affiliation:
University of Memphis, Department of Mathematical Sciences, Memphis, TN 38152-3240, USA (email: awindsor@memphis.edu)
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Abstract

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A sequence of non-negative integers $(\phi _n)_{n =1}^\infty $ is said to be realizable if there is a map T of a set X such that ϕn=#{x:Tnx=x}. We prove that any realizable sequence can be realized by a $C^\infty $ diffeomorphism of $\mathbb {T}^2$.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 3 , June 2008, pp. 1037 - 1041
Copyright
Copyright © Cambridge University Press 2008

References

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