Quadratic maps without asymptotic measure

Hofbauer F, Keller G (1990)

Publication Type: Journal article, Original article

Publication year: 1990

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 127

Pages Range: 319--337

Journal Issue: 2

URI: http://projecteuclid.org/euclid.cmp/1104180141

DOI: 10.1007/BF02096761

Abstract

An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Hofbauer, F., & Keller, G. (1990). Quadratic maps without asymptotic measure. Communications in Mathematical Physics, 127(2), 319--337. https://dx.doi.org/10.1007/BF02096761

MLA:

Hofbauer, Franz, and Gerhard Keller. "Quadratic maps without asymptotic measure." Communications in Mathematical Physics 127.2 (1990): 319--337.

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