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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

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 and Continuous Dynamical Systems, 1998, 4 (1) : 141-158. doi: 10.3934/dcds.1998.4.141
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