A rigorous lower bound for the stability regions of the quadratic map |
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| Authors: | Warwick Tucker Daniel Wilczak |
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| Institution: | aDepartment of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway |
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| Abstract: | We establish a lower bound on the measure of the set of stable parameters a for the quadratic map Qa(x)=ax(1−x). For these parameters, we prove that Qa either has a single stable periodic orbit or a period-doubling bifurcation. From this result, we also obtain a non-trivial upper bound on the set of stochastic parameters for Qa. |
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| Keywords: | Quadratic map Periodic orbit Period-doubling bifurcation Interval analysis |
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