Families of ergodic and exact one-dimensional maps

Author: Barnes Julia  

Publisher: Taylor & Francis Ltd

ISSN: 1468-9375

Source: Dynamical Systems: An International Journal, Vol.22, Iss.2, 2007-06, pp. : 203-217

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Abstract

We give a parametrized family of rational interval maps of degree two, each ergodic, exact and preserving a measure equivalent to a Lebesgue measure. The family includes the unique quadratic Chebyshev polynomial as its only polynomial map. We extend the family to other settings on the circle and real line. We also give numerical approximations to the entropy of the equivalent invariant measure and the Hausdorff dimension of the singular measure of maximal entropy.