Absolutely continuous invariant measures for one-parameter families of one-dimensional maps View Full Text


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Article Info

DATE

1981-09

AUTHORS

M. V. Jakobson

ABSTRACT

Given a one-parameter familyfλ(x) of maps of the interval [0, 1], we consider the set of parameter values λ for whichfλ has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)fλ(x)=λf(x) where 0<λ≦4 andf(x) is a functionC3-near the quadratic mapx(1−x), and ii)fλ(x)=λf(x) (mod 1) wheref isC3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1]. More... »

PAGES

39-88

References to SciGraph publications

  • 1965-07. Invariant sets under iteration of rational functions in ARKIV FÖR MATEMATIK
  • 1981-12. Absolutely continuous measures for certain maps of an interval in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1980-06. On the abundance of aperiodic behaviour for maps on the interval in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1977-02. Applications conservant une mesure absolument continue par rapport àdx sur [0, 1] in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1979-10. Invariant measures for Markov maps of the interval in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1979-06. Sensitive dependence to initial conditions for one dimensional maps in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01941800

    DOI

    http://dx.doi.org/10.1007/bf01941800

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1036786184


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