Asymptotic stability of densities for piecewise convex maps

Tomoki Inoue

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 1, page 83-90
  • ISSN: 0066-2216

Abstract

top
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).

How to cite

top

Tomoki Inoue. "Asymptotic stability of densities for piecewise convex maps." Annales Polonici Mathematici 57.1 (1992): 83-90. <http://eudml.org/doc/262329>.

@article{TomokiInoue1992,
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).},
author = {Tomoki Inoue},
journal = {Annales Polonici Mathematici},
keywords = {Frobenius-Perron operator; asymptotic stability; piecewise convex maps; exactness; stability of densities; theorem of Lasota and Yorke; piecewise convex maps of the unit interval},
language = {eng},
number = {1},
pages = {83-90},
title = {Asymptotic stability of densities for piecewise convex maps},
url = {http://eudml.org/doc/262329},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Tomoki Inoue
TI - Asymptotic stability of densities for piecewise convex maps
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 1
SP - 83
EP - 90
AB - 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).
LA - eng
KW - Frobenius-Perron operator; asymptotic stability; piecewise convex maps; exactness; stability of densities; theorem of Lasota and Yorke; piecewise convex maps of the unit interval
UR - http://eudml.org/doc/262329
ER -

References

top
  1. [1] M. Benedicks and M. Misiurewicz, Absolutely continuous invariant measures for maps with flat tops, Publ. Math. IHES 69 (1989), 203-213. Zbl0703.58030
  2. [2] T. Inoue, Weakly attracting repellors for piecewise convex maps, preprint. Zbl0772.58036
  3. [3] T. Inoue and H. Ishitani, Asymptotic periodicity of densities and ergodic properties for nonsingular systems, Hiroshima Math. J. 21 (1991), 597-620. Zbl0755.28007
  4. [4] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1984. Zbl0606.58002
  5. [5] A. Lasota and J. A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384. Zbl0524.28021
  6. [6] G. Pianigiani, First return map and invariant measures, Israel J. Math. 35 (1980), 32-48. Zbl0445.28016
  7. [7] V. A. Rokhlin, Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. Ser. (2) 39 (1964), 1-36. Zbl0154.15703

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.