Period three orbits for the quadratic family (Q2718008)
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scientific article; zbMATH DE number 1606227
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Period three orbits for the quadratic family |
scientific article; zbMATH DE number 1606227 |
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22 August 2002
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period three orbits
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quadratic family
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quadratic map
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Sharkovskij theorem
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Period three orbits for the quadratic family (English)
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This paper is devoted to period three orbits for the quadratic family. More precisely, the author shows that the quadratic map (1) \(Q_a(x)= a-x^2\) has zero, one, and two period-3 orbits for \(a< 1.75\), \(a=1.75\) and \(a> 1.75\), respectively. Hence the quadratic map \(Q_a\) defined by (1) with \(a\geq 1.75\) has periodic orbits of all periods by the Sharkovskij theorem.
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