Linear integral equations and nonlinear difference-difference equations |
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Authors: | Thomas D. Rogers J.R. Pounder |
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Affiliation: | 1. Department of Mathematics, University of Alberta, Edmonton, Canada T6G 2G1 |
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Abstract: | This paper studies the dynamics of members of the two-parameter family of maps x → μx(1 ? xv), emphasizing the evolution from snapback repeller to crisis bifurcations. The example of the square root map is taken to represent the subfamily where v is fixed and taken from the range . A map from such a subfamily is shown to be conjugate with a map with negative Schwarzian derivative. This allows a characterization of crisis as the demise of a snapback repeller on a proper subinterval. |
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