Far East Journal of Dynamical Systems
Volume 3, Issue 2, Pages 169 - 174
(December 2001)
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TRANSITIVITY AND A PERIODIC POINT DO NOT IMPLY SENSITIVITY
Ming-Chia Li (Taiwan)
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Abstract:
In [Rocky Mountain J. Math. 22 (1992), 353-375], it is proved that, on a circle, any transitive map with a periodic point has sensitive dependence on initial conditions. In this paper, we show that above result may not be true for maps on other spaces by constructing a subsystem of the Bebutov system. Although not sensitive, this subsystem has complicated dynamics. |
| Keywords and phrases: chaos, transitivity, sensitivity, bebutov’s system. |
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