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2021 Some Results on Invariant Measures for $1$-dimensional Maps
Fritz SCHWEIGER
Tokyo J. Math. Advance Publication 1-18 (2021). DOI: 10.3836/tjm/1502179353

Abstract

For many fibred systems the existence of an invariant measure can be proved but considerably less is known about the shape of the density. In this note various examples of invariant densities are discussed: Piecewise fractional linear maps with four branches and maps which are associated to continued fractions with increasing digits. There are ergodic maps with a non-integrable density which do not have an indifferent fixed point and maps such that the set of points which miss the digit $k=1$ has positive Lebesgue measure.

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Fritz SCHWEIGER. "Some Results on Invariant Measures for $1$-dimensional Maps." Tokyo J. Math. Advance Publication 1 - 18, 2021. https://doi.org/10.3836/tjm/1502179353

Information

Published: 2021
First available in Project Euclid: 4 October 2021

Digital Object Identifier: 10.3836/tjm/1502179353

Subjects:
Primary: 11K55
Secondary: 28D05, 37A05

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

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