Dynamics of functions with an eventual negative Schwarzian derivative

Benjamin Webb

doi:10.3934/dcds.2009.24.1393

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2009, Volume 24, Issue 4: 1393-1408. Doi: 10.3934/dcds.2009.24.1393

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Dynamics of functions with an eventual negative Schwarzian derivative

Benjamin Webb^1,

1.
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30322

Received: April 30, 2008

Revised: December 31, 2008

Published: October 2009

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Abstract

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:

One dimensional dynamics,
eventual negative Schwarzian derivative.

Mathematics Subject Classification: Primary: 37E05; Secondary: 37N25.

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