Asymptotic stability of densities for piecewise convex maps

• Autorzy: Tomoki Inoue
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Frobenius-Perron operator; asymptotic stability; piecewise convex maps; exactness

Kategorie tematyczne

• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 1
• Strony: 83-90

Daty

wydano

1992

otrzymano

1991-05-10

Twórcy

autor

Tomoki Inoue

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

Bibliografia

• [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.