2019
Том 71
№ 8

All Issues

Snoha L.

Articles: 1
Article (English)

Full cascades of simple periodic orbits on the interval

López V. Jiménez, Snoha L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 12. - pp. 1628-1637

Any continuous interval map of type greater than 2∞ is shown to have what we call a full cascade of simple periodic orbits. This is used to prove that, for maps of any types, the existence of such a full cascade is equivalent to the existence of an infinite ω-limit set. For maps of type 2∞, this is equivalent to the existence of a (period doubling) solenoid. Hence, any map of type 2∞ which is either piecewise monotone (with finite number of pieces) or continuously differentiable has both a full cascade of simple periodic orbits and a solenoid.