Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: generic chaos

Sortuj według:

Ogranicz wyniki do:

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

100%

Piórek J.

Annales Polonici Mathematici

1996

tom 63

nr 2

167-172

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.

A note on generic chaos

51%

Liao G.

Annales Polonici Mathematici

1994

tom 59

nr 2

99-105

We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.

Defining complete and observable chaos

44%

López V.

Annales Polonici Mathematici

1996

tom 64

nr 2

139-151

For a continuous map f from a real compact interval I into itself, we consider the set C(f) of points (x,y) ∈ I² for which $lim inf_{n→∞} |f^n(x) - f^n(y)| = 0$ and $lim sup_{n→∞} |f^n(x) - f^n(y)| > 0$. We prove that if C(f) has full Lebesgue measure then it is residual, but the converse may not hold. Also, if λ² denotes the Lebesgue measure on the square and Ch(f) is the set of points (x,y) ∈ C(f) for which neither x nor y are asymptotically periodic, we show that λ²(C(f)) > 0 need not imply λ²(Ch(f)) > 0. We use these results to propose some plausible definitions of "complete" and "observable" chaos.

Ograniczanie wyników

3 Annales Polonici Mathematici

1 Liao G.

1 López V.

1 Piórek J.

2 1996

1 1994

Wyniki wyszukiwania

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

A note on generic chaos

Defining complete and observable chaos