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ArticleOriginal scientific text

Title

Asymptotic stability of densities for piecewise convex maps

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima, Hiroshima 724, Japan

Abstract

We study the asymptotic stability of densities for piecewise convex maps with flat bottoms or a neutral fixed point. Our main result is an improvement of Lasota and Yorke's result ([5], Theorem 4).

Keywords

ENG
Frobenius-Perron operator, asymptotic stability, piecewise convex maps, exactness

Bibliography

  1. M. Benedicks and M. Misiurewicz, Absolutely continuous invariant measures for maps with flat tops, Publ. Math. IHES 69 (1989), 203-213.
  2. T. Inoue, Weakly attracting repellors for piecewise convex maps, preprint.
  3. T. Inoue and H. Ishitani, Asymptotic periodicity of densities and ergodic properties for nonsingular systems, Hiroshima Math. J. 21 (1991), 597-620.
  4. A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1984.
  5. A. Lasota and J. A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384.
  6. G. Pianigiani, First return map and invariant measures, Israel J. Math. 35 (1980), 32-48.
  7. V. A. Rokhlin, Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. Ser. (2) 39 (1964), 1-36.
Annales Polonici Mathematici
1992/57/1
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Pages:
83-90
Main language of publication
English
Received
1991-05-10
Published
1992
Exact and natural sciences