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

• Autorzy: Józef Piórek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generic chaos  

Kategorie tematyczne

• 54H20: Topological dynamics
• 26A18: Iteration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 2
• Strony: 167-172

Daty

wydano

1996

otrzymano

1994-11-10

poprawiono

1995-01-12

poprawiono

1995-03-10

Twórcy

autor

Józef Piórek

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] R. M. Corless, Continued fractions and chaos, Amer. Math. Monthly 99 (1992), 203-215.
• [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.
• [4] G. Liao, A note on generic chaos, Ann. Polon. Math. 59 (1994), 101-105.
• [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.
• [7] J. Piórek, On generic chaos of shifts in function spaces, Ann. Polon. Math. 52 (1990), 139-146.
• [8] J. Piórek, On weakly mixing and generic chaos, Univ. Iagell. Acta Math. 28 (1991), 245-250.
• [9] J. Piórek, Ideal gas is generically chaotic, Univ. Iagell. Acta Math.. 32 (1995), 121-128.
• [10] L. Snoha, Generic chaos, Comment. Math. Univ. Carolin. 31 (1990), 793-810.