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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

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.
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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