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A local limit theorem for a sequence of interval transformations

Published online by Cambridge University Press:  19 September 2008

P. Calderoni ,
M. Campanino  and
D. Capocaccia
P. Calderoni
Affiliation:
ZiF, Universität Bielefeld, 4800 Bielefeld, West Germany
M. Campanino
Affiliation:
ZiF, Universität Bielefeld, 4800 Bielefeld, West Germany
D. Capocaccia
Affiliation:
Instituto Matematico ‘G. Castelnuovo’, Università di Roma, 00185 Roma, Italy
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Abstract

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Let λ > 1 be a real eigenvalue of an automorphism of the two dimensional torus. We prove that for a dense, open subset of intervals the sequence where {x} denotes the fractional part of x and χ[a, b] the characteristic function of [a, b], satisfies the local limit theorem with respect to Lebesgue measure on [0, 1].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 185 - 201
Copyright
Copyright © Cambridge University Press 1985

References

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