Periodic and limit orbits and the depth of the center for piecewise monotone interval maps

Nitecki, Zbigniew

doi:10.1090/S0002-9939-1980-0581016-9

Periodic and limit orbits and the depth of the center for piecewise monotone interval maps
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Proc. Amer. Math. Soc. 80 (1980), 511-514 Request permission

Abstract:

For a piecewise monotone map of the interval: (a) the nonwandering points outside the closure of the periodic points are isolated in the nonwandering set; (b) the forward orbit of any such point misses all turning points; (c) the depth of the center is at most 2; and (d) all $\omega$-limit points belong to the closure of the periodic points.

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