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Periodic points and invariant pseudomeasures for toral endomorphisms

Published online by Cambridge University Press:  19 September 2008

William A. Veech
William A. Veech
Affiliation:
Department of Mathematics, Rice University, Houston, Texas 77251, USA
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Abstract

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Extending a result of Livsic [10] it is proved that the coboundary equation f(Tx)−f(x) = g(x) admits a C∞ solution f for C∞g when T is an ergodic toral endomorphism and g sums to zero over every periodic orbit. The same statement is false with C1 in place of C∞, in contrast to the Livsic (hyperbolic) theorem. In one dimension the ‘Lip α’ case leads to questions relating to the generalized Riemann hypothesis.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 3 , September 1986 , pp. 449 - 473
Copyright
Copyright © Cambridge University Press 1986

References

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