Dense set of negative Schwarzian maps whose critical points have minimal limit sets

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January 1998, 4(1): 141-158. doi: 10.3934/dcds.1998.4.141

Dense set of negative Schwarzian maps whose critical points have minimal limit sets

Alexander Blokh ^1, and Michał Misiurewicz ^2,

1.	Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, AL 35294-1170
2.	University of Alabama in Birmingham and Indiana University - Purdue University Indianapolis, United States

Received March 1997 Published October 1997

Abstract
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We study $C^2$-structural stability of interval maps with negative Schwarzian. It turns out that for a dense set of maps critical points either have trajectories attracted to attracting periodic orbits or are persistently recurrent. It follows that for any structurally stable unimodal map the $\omega$-limit set of the critical point is minimal.

Keywords: negative Schwarzian, Interval maps, structural stability, persistent recurrence..

Mathematics Subject Classification: 58F03, 58F1.

Citation: Alexander Blokh, Michał Misiurewicz. Dense set of negative Schwarzian maps whose critical points have minimal limit sets. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 141-158. doi: 10.3934/dcds.1998.4.141

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