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November  2009, 24(4): 1393-1408. doi: 10.3934/dcds.2009.24.1393

Dynamics of functions with an eventual negative Schwarzian derivative

Benjamin Webb 1,

1. 

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30322, United States

Received  May 2008 Revised  January 2009 Published  May 2009

In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this paper we consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. The introduction of this class was motivated by some maps arising in neuroscience.
Keywords: eventual negative Schwarzian derivative., One dimensional dynamics.
Mathematics Subject Classification: Primary: 37E05; Secondary: 37N2.
Citation: Benjamin Webb. Dynamics of functions with an eventual negative Schwarzian derivative. Discrete & Continuous Dynamical Systems, 2009, 24 (4) : 1393-1408. doi: 10.3934/dcds.2009.24.1393
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