Summary
This article contains a proof of the existence of SBR measures for the family of maps of the plane known as Lozi maps: L(x, y) = (1-a׀x׀+y, bx). We also prove that the number of SBR measures is finite. Our approach also yields invariant measures for other classes of dynamical systems like piecewise expanding mappings of an interval with infinitely many pieces and Hölder derivative. Although known to specialists from my 1983 dissertation (University of California, Berkeley), the results presented in this article have never been published. I am delighted that the article found its place in the current volume, as the ideas of several papers that Jim Yorke co-authored or inspired played an important role in my approach.
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Rychlik, M. (2004). Invariant Measures and the Variational Principle for Lozi Mappings. In: Hunt, B.R., Li, TY., Kennedy, J.A., Nusse, H.E. (eds) The Theory of Chaotic Attractors. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21830-4_13
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DOI: https://doi.org/10.1007/978-0-387-21830-4_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2330-1
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