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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

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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

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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

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  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

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