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

Józef Piórek

Annales Polonici Mathematici (1996)

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

Abstract

top
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.

How to cite

top

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

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.