# An example of a genuinely discontinuous generically chaotic transformation of the interval

Annales Polonici Mathematici (1996)

- Volume: 63, Issue: 2, page 167-172
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topJózef Piórek. "An example of a genuinely discontinuous generically chaotic transformation of the interval." Annales Polonici Mathematici 63.2 (1996): 167-172. <http://eudml.org/doc/262628>.

@article{JózefPiórek1996,

abstract = {It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.},

author = {Józef Piórek},

journal = {Annales Polonici Mathematici},

keywords = {generic chaos},

language = {eng},

number = {2},

pages = {167-172},

title = {An example of a genuinely discontinuous generically chaotic transformation of the interval},

url = {http://eudml.org/doc/262628},

volume = {63},

year = {1996},

}

TY - JOUR

AU - Józef Piórek

TI - An example of a genuinely discontinuous generically chaotic transformation of the interval

JO - Annales Polonici Mathematici

PY - 1996

VL - 63

IS - 2

SP - 167

EP - 172

AB - It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.

LA - eng

KW - generic chaos

UR - http://eudml.org/doc/262628

ER -

## References

top- [1] R. M. Corless, Continued fractions and chaos, Amer. Math. Monthly 99 (1992), 203-215. Zbl0758.58020
- [2] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, New York, 1982.
- [3] T. Gedeon, Generic chaos can be large, Acta Math. Univ. Comenian. 54-55 (1988), 237-241. Zbl0725.26006
- [4] G. Liao, A note on generic chaos, Ann. Polon. Math. 59 (1994), 101-105. Zbl0810.54032
- [5] R. Mañé, Ergodic Theory and Differentiable Dynamics, Springer, Berlin, 1987.
- [6] J. Piórek, On the generic chaos in dynamical systems, Univ. Iagell. Acta Math. 25 (1985), 293-298. Zbl0587.54061
- [7] J. Piórek, On generic chaos of shifts in function spaces, Ann. Polon. Math. 52 (1990), 139-146. Zbl0719.58005
- [8] J. Piórek, On weakly mixing and generic chaos, Univ. Iagell. Acta Math. 28 (1991), 245-250. Zbl0746.58059
- [9] J. Piórek, Ideal gas is generically chaotic, Univ. Iagell. Acta Math.. 32 (1995), 121-128. Zbl0832.58032
- [10] L. Snoha, Generic chaos, Comment. Math. Univ. Carolin. 31 (1990), 793-810. Zbl0724.58044

## NotesEmbed ?

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