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Some counterexamples in topological dynamics

Published online by Cambridge University Press:  01 August 2008

RONNIE PAVLOV
RONNIE PAVLOV*
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA (email: rpavlov@math.ubc.ca)
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Abstract

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In this paper, we exhibit, for any sparse-enough increasing sequence {pn} of integers, totally minimal, totally uniquely ergodic, and topologically mixing systems (X,T) and (X′,T′) and f∈C(X) for which the averages $({1}/{N}) \sum _{n=0}^{N-1} f(T^{p_n} x)$ fail to converge on a residual set in X, and where there exists x′∈X′ with $x.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 4 , August 2008 , pp. 1291 - 1322
Copyright
Copyright © 2008 Cambridge University Press

References

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